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Fluid Mechanics Homework Help By TutorBin

Manometry & Buoyancy	Forces on submerged surfaces
Elementary fluid dynamics- Bernoulli equation	Mass, Momentum, and Energy conservation
Continuity & Jet stability	Dimensional Analysis
Navier-Stokes equation	Interfacial phenomena
Laminar & Turbulent flow	Frictional losses in pipes and pipe fittings

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Recently Asked Fluid Mechanics Questions

Expert help when you need it

Q1:Problem: Water flows through a turbine (T) from reservoir A to reservoir B, as shown in the figure. Determine how much power is the turbine able to generate and provide to the electric grid (turbine efficiency = 0.70) for a discharge Q of 2.2 m3/s? Also, sketch the energy grade line (EGL), indicating all energy losses, changes in slope, and abrupt changes. Make sure your figure can be interpreted even if it is not perfect. Assume the pipe material is cast iron with roughness Kg = 0.25 mm, kinematic viscosity v= 10-6 m2/s, the coefficient for entrance losses Ke = 0.5, and a= 1. ZA= 780 m A ZB= 80 m 1 = D1 = 1.5 m L1 = 690 m B T D2= 0.8 m L2= 4100 mSee Answer
Q2:1. As part of your role at a heavy-goods vehicle manufacturer, you have been asked to determine the drag caused by the boundary layer developing along a section of the trailer roof, which can be treated as having constant pressure, as the truck travels at 10 m/s. The velocity profile in this region is given by: u- us 2/7 +A ++1)+B where us is the velocity at the edge of the boundary layer. A and B are constants. a) How many primary and auxiliary boundary conditions need to be satisfied? What values must A and B take such that these boundary conditions are satisfied? [8 marks] b) By evaluating the ratio between the displacement thickness (8*) and the momentum thickness (0) of the boundary layer, determine whether the boundary layer on the trailer roof is laminar or turbulent. [7 marks] c) The thickness of the boundary layer at locations x = 0.1 m and 0.5 m is measured using Pitot probe data to be 8 = 4 mm and 8 = 14.5 mm, respectively. Calculate the displacement and momentum thicknesses at these locations. [4 marks] d) The trailer roof has width 2 m. Use the von Karman integral momentum equation to determine the total drag contribution due to the boundary layer between x = 0.1 m and 0.5 m. Assume p = 1.3 kg/m3. [6 marks] 2. You work for an aerospace company which is due to start testing a design in a supersonic wind tunnel. It is a two-dimensional, blow down wind tunnel with rectangular cross-section. The width of the wind tunnel is 100mm and the height at key points is provided in Figure Q2a. At x = 0 mm, the stagnation pressure is always 175 kPa and the stagnation temperature is 300 K. Prior to your test entry, you are given calibration data measured using a Pitot probe mounted in the centre of the test section during wind tunnel start up when the wind tunnel is empty. Your task is to evaluate whether the readings provided by the Pitot probe are sensible to check whether it is working correctly. You can neglect boundary-layer effects throughout this question. a) During supersonic wind tunnel operation, the Mach number in the test section of the tunnel is 2.5. By considering the area ratio between the test section and the throat. determine the height, h, at the throat (x = 50 mm). b) When the peak Mach number in the wind tunnel is 1, what is the stagnation pressure at the Pitot probe location, x = 600 mm? c) When a normal shock wave is in the test section at x = 400 mm, what is the Mach number of the flow ahead of this shock wave? What is the stagnation pressure before and after the shock? d) The wind tunnel starts at time t = 2 s and shuts down at time, t = 15 s. The normal shock wave crosses the Pitot probe at t = 10 s. You are given Figure Q2b, which shows the pressure measured by the Pitot probe as a function of time. Annotate the key timings on a copy of this graph and describe what these correspond to in terms of the tunnel flow. Also explain (with the help of sketches) whether the Pitot probe is functioning correctly. [7 marks] [4 marks] [6 marks] [8 marks] 3. You are on a placement in a chemical plant and have been asked to calculate the force on the walls of a circular pipe (radius, R = 0.02 m) using pressure tappings at the two stations (A and B) shown in Figure Q3. The chemical in the pipe has viscosity, u = 5 x 10-3 kg / m s, and density, p = 660 kg/m3. The pressure tappings are separated by a distance, L = 20 m, and are connected to a manometer filled with water (p = 1000 kg/m3) with an indication, Ah = 40 mm. a) Is the pressure at B higher or lower than the pressure at A? For g = 9.8 m/s2, calculate the magnitude of this pressure change. [7 marks] b) The flow in the pipe is laminar and fully developed, so can be assumed to follow a Hagen-Poiseuille distribution: u = 4 4u dx 1 ªP -(r2 - R2) What is the velocity at point 1 in section B, which is located 0.01 m away from the pipe axis? [5 marks] c) What is the maximum velocity across the cross-section at station B? What is the maximum velocity at station A? [7 marks] d) Recall that the critical Reynolds number for transition in pipes occurs at Reynolds numbers based on the diameter in the range Rep = 2300 - 3500. Explain whether our assumption of laminar flow is reasonable. [6 marks] A L B 0.01 m chemical Y Ah water Figure Q3: Chemical flow through a pipe 1 R 4. You are responsible for the design of the convergent nozzle for a turbojet engine fitted to a civil aircraft, as shown in Figure Q4. During operation at an altitude of 10,000 m, the aircraft flies at 300 m/s and the flow exhausts to atmosphere, where the pressure is 26.5 kPa and the temperature is 223 K. In this question, you should treat the flow as quasi-one-dimensional and inviscid. a) The radius of the nozzle satisfies the equation R(x) = 2-0.44 x2 where both x and R are expressed in metres. What is the area ratio between the nozzle inlet (x = 0.0 m) and the nozzle exit (x = 1.5 m)? b) The turbine exit temperature is the stagnation temperature, To = 400 K, of the flow in the nozzle. Similarly, the turbine exit pressure is the stagnation pressure, Po, of the flow in the nozzle. When the turbine exit pressure is 35 kPa, what is the Mach number at the nozzle exit? c) In a different scenario, the turbine exit pressure is 70 kPa. What is the Mach number of the flow at the nozzle exit? Also determine the Mach number at the nozzle inlet. d) The turbo-machinery team within the company have asked you to specify what exit pressure of the turbines results in perfectly expanded flow, with minimal expansion and compression waves outside the nozzle. What is this turbine exit pressure? [6 marks] [6 marks] [7 marks] [6 marks] combustion compressor chamber turbine nozzle p = 26.5 kPa T = 223 K capture streamtube p = 26.5 kPa T = 223 K Ro nozzle inlet, nozzle exit, x = 0.0 m x = 1.5 m Figure Q4: Diagram of turbojet engine 100 mSee Answer
Q3:EACH QUESTION IS WORTH 12.5 POINTS. QUESTION 6.3.7 IS A BONUS QUESTION FOR 10 POINTS. 6.1.1. Using the time and space criteria, classify the following open channel flow scenarios (steady or unsteady and uniform or varied): a. Constant flow in a long, prismatic channel with a mild slope. b. Flow in the transition of the channel in part (a) to a channel with a steep slope. c. Flow on a sloped parking lot during a uniform-intensity rainfall event. d. Flow on a sloped parking lot during a rainfall event that decreases in intensity over time. e. Flow in a prismatic channel from a rapidly opening sluice gate. f. Flow during the dry season in an urban (natural) stream. 6.2.1. A concrete channel with an unusual cross section carries water at a flow rate of Q=30 m3/s. Determine the channel's slope. Use table 6.2 to find manning coefficient 4.0 m 1.6 m 3.6 m 2.0 m 6.2.4. A 3-m-wide rectangular irrigation channel carries a discharge of Q= 50 m3/s. The channel has a slope of 0.041 and a Manning's coefficient is n=0.022. Determine the normal depth using successive substitution. 6.2.8. Uniform flow occurs in a 20-ft-wide rectangular channel with a discharge of 2,520 cfs. If the normal depth of the flow is 15 ft, what will be the new normal depth when the width of the channel expands to 30 ft? Assume that the slope and channel roughness remain constant in both channels. 6.2.9. Determine the diameter of a corrugated-metal, storm water pipe that is designed to carry a flow rate of 5.83 m3/s while flowing half full. The slope of the pipe is 0.02 m/m and uniform depth is assumed. Also, determine the pipe size required to carry the same flow rate if the pipe is to flow full. HINT: A = (1/8)(20 - sin 20)do2; and P = 0do 6.2.10. Design a trapezoidal channel and a rectangular channel to convey 100 cfs on a slope of 0.002. Both channels are lined with concrete. Specify width, depth, and side slopes. In both cases, try to obtain channels where the depth is about 60% of the bottom width. 6.3.2. Design the best hydraulic (rectangular) section for a metal channel to carry a flow rate of 31.2 cfs on a slope of 0.04. 6.3.3. An open channel (n=0.011) is to be designed to carry 7.14 m3/s on a slope of 0.0063. Find the diameter of the best hydraulic section (semicircle). HINT: A = (1/8)(20 - sin 20)do2; and P = 0do 6.3.7. Determine the side slopes of the best hydraulic (triangular) section.See Answer
Q4:CEE 341 Fluid Mechanics for Civil Engineers Homework # 6 Problem 1 In a lab experiment, it has been found that the velocity profile in a pipe where the flow is turbulent (this will be defined in the next module) is: V = Vmax ¥ (1-2)", where Vmax is the maximum velocity in the centerline of the pipe; r is the radial distance from the pipe centroid; ro is the radius; and n is an exponent that depends on the flow condition and that varies between 1/6 to 1/8. Derive a formula for the kinetic energy correction coefficient a for the given velocity profile. What is a if n = 1/6? Problem 2 A pipe is attached to a tank and discharges water in the atmosphere as shown in the figure. The head losses up to point B are 0.4 m, the head losses up to the nozzle are 1 m, and the kinetic energy correction factor a is 1 everywhere. (1) What is the discharge? (2) What is the value of pressure at B? 1.5 m Water B + 40 cm diameter 3.5 m 1 «20 cm-diameter nozzle 1 Problem 3 A pipe with a venturi meter withdraws water from a tank as shown in the figure. Find the head losses at the throat of the venturi meter under these conditions: - Cavitation is just about to occur at the throat of the venturi meter. The vapor pressure of water at 20 °℃ is 2340 Pa abs. - Velocity in the portion of the pipe with diameter D is 4 m/s. D = 30 cm, d = 15 cm, Patm = 100 kPa, H = 5 m. - Assume steady flow and a = 1.0 everywhere. H D 1 Water T=20°C 0 Problem 4 A pump draws water from a tank (point A in the figure) through a pipe with diameter D = 20 cm, and discharges it into air at point C. Find the height h from the water surface to C (see figure) when: - Velocity in C is 3 m/s; - The pump receives 42 kW from the electric grid and operates at 63% efficiency; - The head loss in the pipe between A and C is 1.5 * V2/g; - a = 1 at all locations. C h Pump A Y Water 2 dSee Answer
Q5:MAE 242 Summer 2024 HW5 Problem 1: Consider the pipe system presented here. You have fluid flowing into a pipe at Point A. Point B is capped, so no fluid is flowing out of the top of the pipe. There are two outlets: Point C and Point D. If water flows in the Pipe at Point A with a Velocity at 8 m/s and has a diameter of 100 mm. The outflow pipes at Point C and Point D each have a diameter of 20 mm. The height of the pipe is 5 meters. Determine the Velocity at Point D and Point C. What is the pressure of the fluid in the Pipe at Point A? Point B Point D Point C Point A Problem 2: A milkshake has fairly similar density to that of water (p = 1200 kg/m3) but is far more viscous with µ = 1 kg/m*s. d Part A: Say you try to drink a milkshake through a straw that is 30 cm long and 5 mm in diameter. Your lungs are capable of creating a vacuum pressure of 3000 Pa. (Vacuum pressure just means a pressure below that of the atmosphere, so Plung = Patm - 3000 Pa.). You find that if you place the straw just at the surface of the liquid, you are unable to suck the milkshake through the straw, but if you push the straw deeper into the shake, you can. To what depth, d, would you need to push the straw in order to just start to sip the milkshake? Part B: Suppose you push the straw to a depth of 10 cm and suck with a suction pressure of -3000 N/m2. What volume flow rate of milkshake can you produce through the straw? Hint: You may want to use a pseudo-streamline with station 1 at the surface of the milkshake. You also might want to assume you have laminar flow through the straw, which you can check once you have a solution.See Answer
Q6:6. In a V-G meter, we get readings of 21 at 300 rpm and 33 at 600 rpm. a. Calculate the plastic viscosity and yield strength using the Bingham plastic model. b. Calculate the consistency and flow-behavior indices using the power law model. c. Derive and expression which gives you K and n from up and Ty.See Answer
Q7:4. We are drilling at 10000 ft in a formation with 20% porosity, 30% water saturation and 70% gas saturation. The temperature is 640 R, and the mud density is 11 ppg. The gas gravity is .72. The drilling rate is 100 ft/hr with a 12 % inch bit. The circulation rate is 300 gpm. Formation water is 9.04 ppg, and formation rock density is 26 ppg. a. What is the mud density at the surface? Ppg b. What is the average density of the annular mud? c. At what rate (SCFD) will gas be liberated at the surface?See Answer
Q8:1. We have a mud pump (triplex) with an 8 inch liner and a 12 inch stroke. The volumetric efficiency is 89% and we are running at 50 spm. a. What is the pump factor (gal/cycle)? (remember its TRIplex .. 3 liners) b. What is the flowrate? (gpm) c. What is the delivered hydraulic horsepower? d. What is the brake horsepower at the motor if the mechanical efficiency of the pump is 80%?See Answer
Q9: FLUIDS MECHANICS LABORATORY THE HYDRAULICS BENCH The Hydraulics Bench is a service module designed to accommodate a range of accessories, each of which demonstrates an aspect of hydraulic theory. A self-priming centrifugal pump draws water from the sump tank and delivers into a vertical transparent pipe. A panel mounted bench control valve is used to regulate the flow in the delivery pipe which terminates in a quick release pipe connector situated in the bed of a channel. Water discharging from the accessory on test is collected in the volumetric measuring tank. This tank is stepped to accommodate low or high flow rates and incorporates a stilling baffle to reduce turbulence. MEASUREMENT OF VOLUMETRIC FLOW RATE The molded bench top incorporates a volumetric measuring tank which is stepped to accommodate low or high flow rates. A remote sight gage, consisting of a sight tube and scale is connected to a tap in the base of the tank, and gives an instantaneous indication of water level. The scale is divided into two zones corresponding to the volume above and below the step in the tank. To make a volumetric flow reading, the ball of the dump valve is lowered, retaining the water in the tank. Timings are taken as the water level rises in the tank. Low flow rates are monitored on the lower portion of the scale corresponding to the small volume beneath the step. Larger flow rates are monitored on the upper scale corresponding to the main tank. When not used for volumetric determinations, the water drains back to the sump by lifting the dump valve. F1-10 Hydraulics Bench Drain Valve 0 Water Inlet Stilling Baffle Sight Tube and Scale Location of Hook & Point H Centrifugal Service Pump Bench Control Valve Weir Carrier J Stilling Baffle Dump Valve RCD Pump ON/OFF Switch E1: THE IMPULSE MOMENTUM PRINCIPLE (Impact of a Jet) LEARNING OBJECTIVES Demonstrate experimentally the impulse-momentum principle (linear-momentum equation). Calculate the force generated by a jet of water as it strikes a flat plate or a hemispherical cup and compare with the momentum change of the jet. THEORY OF THE EXPERIMENT For a given control volume (c.v) with a control surface (c.s) that completely surrounds the control volume, the Reynolds transport theorem for steady flow is: days = √nph-VdA dt where the integral is over the control surface and the symbols and variables mean: Nsys = Extensive quantity (any property of the flow, e. g., mass, velocity, etc.) t = time (s) n = Intensive quantity: refers to Nsys per unit of mass [kg] p = Density of the flow [1] f = unit direction vector V = Velocity vector and V = Velocity [] A = Area [m²] Newton's second law, referred to as the momentum equation, states that the resultant force acting on a system equals the rate of change of momentum of the system when measured in an inertial reference frame. Replacing with V, this becomes: ΣF=SU = sum of all forces acting on the control volume = [pV(V-n)dA C.S Vout J Figure 1: A jet of water impinging on a flat plate V₁lak Z = H Z=O When applying this general equation to the conservation of linear momentum for the case of a jet impinging on a flat plate (Figure 1), we get: where N is the number of flow exit/entrance areas and fi is the unit vector normal to the control area. For the entrance to the control volume, f = -1 relative to the flow of the jet of fluid. It then follows for a vertically upward jet: F(-1)= PQin (1) Vin (1)(-1) F = PQin Vin where Qin = Q = Volumetric flowrate [T Ĵ= unit direction vector p= Density of the flow Vin = Vplate = ? Σ F₁ = Σ P₁AiV₁ (V₁-A) R=Σ PiA¡Vi The velocity of the jet as it strikes the plate, Vplate, is less than the exit velocity at the nozzle, Vjat, because of the deceleration due to gravity. We can apply Bernoulli's equation to determine Vplate- PV² For Bernoulli's Equation + P 2 + gh = constant (along a streamline) the following assumptions apply: P Y Vi _ Vi V² = [kg] Assumptions of Bernoulli's Equation for the impact of a jet No shaft work • No heat transfer Steady flow Incompressible flow (p = constant) Frictionless flow Applying Bernoulli's equation yields: P₁V² + 2 = P₂²_V₂² P, Y2g Y 2g = - Pressure Head 2g 2g Vi _ V₁ + H 2g 2g +2₂ V₂ = √V²-2gH V₁ =VjV₂ = Vplate or V₂ cup V₂ 2g . - Velocity Head Flow along the streamline z = Elevation Head Hence, F=PQV=PQ √V-2gH Vat Figure 2: A jet of water impinging on a hemispherical cup. Qin = -20o and Vin = -Vout F = PQin (Vin +Vout) = 2pQinVin 2n = Q = volumetric flowrate p = density of fluid [kg ŉ always points out of the volume = -1 at the entrance and exit. F(-ĵ) = pQ_(†)V_(†)(−1) + pQout (-Ĵ)V out (-Ĵ)(−1) + µQ…(−Ĵ)V…(-Ĵ)(−1) -F=-pQV₁ -2pQmVant == וון CV V₂ - V - √V²-28 H = = g in F=2pQ√ √V-2 g H Z-H When applying this general equation to the conservation of linear momentum for the case of a jet impinging on a hemispheric cup (Figure 2), we get: ΣF₁ = [p,4,V, (V₁.ñ) 3. S Neur 'cup V₂-p Ajel Z=H Experimental Procedure Figure 3 presents the experimental apparatus. The inlet nozzle is housed in a transparent cylinder, the interior of which remains at atmospheric pressure due to air vents in the top plate. The pump draws water from the sump tank and this water issues from the nozzle at a flow rate that is regulated by the bench control valve. The water strikes the target (flat plate or hemispherical cup) and the mass loaded in the weight pan is used to determine the force needed to balance that from the water jet. The deflected water then exits through outlet holes into the tank where the time taken to collect a certain volume is used in the calculation of the volumetric flow rate. flow control valve weight hanger Spring motor Air Vent Knurled nuts Top Plate A tank pivot CG- pump weigh tank plug sump tank Weight Pan Level Gauge Spirt Level Target Plate Nozzle Tank Figure 3: Impact of a jet apparatus. (Images from http://www.armfield.co.uk/images/fl 16 rgb.jpg)See Answer
Q10:6) Problem 2.20 (from textbook); 2.20 Rheology of Hyaluronic Acid Hyaluronic acid is a high-molecular polymer of the repeating disaccharide units glucuronic acid and N-acetylglucosamine. Present in all tissues and usually linked with protein in the form of proteoglycans, hyaluronic acid is a component of the synovial fluid that is present between joints and is thought to play a role in joint lubrication and resisting compressive forces. (a) The data in the table at the bottom of this page were obtained at 25°C in a cone-and-plate visco- meter for solutions of 5 mg mL-¹ hyaluronic acid in phosphate-buffered saline with a pH of 7.2. Deter- mine whether the fluid behaves as a power law fluid, and if so, determine the parameters m and n. (b) The hyaluronic acid solution was treated with the enzyme hyaluronidase for 5 minutes at 25°C, and the data on the right-hand side of the table were recorded. Determine the effect of the enzyme upon the rheology of hyaluronic acid. (c) Explain why the enzyme might change the rheology of hyaluronic acid. Hyaluronic acid Shear rate (s¹) Shear stress (dyn cm2) 2.39 4.28 6.23 8.05 3.75 7.50 11.3 15.0 22.5 30.0 37.5 11.2 14.1 17 Hyaluronic acid plus hyaluronidase Shear stress (dyn cm 2) Shear rate (s) 375 450 525 600 750 900 1,125 3.31 3.93 4.48 5.10 6.37 7.79 9.61 Please use excel or any other graphical computational tool to draw the plots (hand drawn approximate plots are not acceptable).See Answer
Q11:3) The velocity vector of a fluid is given as v = (2s ¹x +3ms³t²)i + (10m-²s-¹y3 + 2ms-³t2)j, where i and j are the unit vector in x and y direction, where x and y are in meters and t is in seconds. Is the fluid flow (i.e., velocity) in steady state or unsteady state? Is it two-dimensional or three dimensional? • Compute the total acceleration along with local and convective acceleration in x, y, and z direction at x = 4m, and y=-1m, when t = 2s. What magnitude of the overall acceleration in this condition?See Answer
Q12:2) Problem 2.5 (from textbook) 2.5 For steady flow through a conical nozzle of length L, the velocity in the direction of flow, x direction, is approximately x₁ - U₂ (1-2) Vx = (2.10.4) where Uo is the velocity at the entrance to the nozzle. (a) Determine the acceleration in the x direction at x = 1 m for U₁ = 5 ms¹ and L=2 m. (b) The velocity given by Equation (2.10.4) is approxi- mate. Identify two locations along the nozzle where the velocity will not be correct.See Answer
Q13:2.8.28 Figure P2.8.28 is a representation of the Keswick gravity dam in California. Find the magnitudes and locations of the hydrostatic forces acting on the headwater vertical wall of the dam and on the tailwater inclined wall of the dam. Note that the slope given is the ratio of the run to the rise. Consider a unit length of the dam (b = 1 ft). Headwater 100 ft 21.5 ft EI. 595.00 ft EI. 565.40 ft Slope - 0.7:1 Tailwater El. 491.00 ft FIGURE P2.8.28 Z 30 ftSee Answer
Q14:2.8.11 WP Determine the magnitude and direction of the force that must be applied to the bottom of the gate shown in Fig. P2.8.11 to keep the gate closed. 2.1 m Water 2-m-wide gate Hinge 0.8 m FIGURE P2.8.11See Answer
Q15:2.6.17 WP SS The cylindrical tank with hemispherical ends shown in Fig. P2.6.17 contains a volatile liquid and its vapor. The liquid density is 800 kg/m³, and its vapor density is negligible. The pressure in the vapor is 120 kPa (abs), and the atmospheric pressure is 101 kPa (abs). Determine: (a) the gage pressure reading on the pressure gage, and (b) the height, h, of the mercury in the manometer. 1 m + 1 m Vapor 1 m Liquid FIGURE P2.6.17 Open h MercurySee Answer
Q16:2.6.7 WP The U-tube manometer shown in Fig. P2.6.7 has two fluids, water and oil (S = 0.80). Find the height difference between the free water surface and the free oil surface with no applied pressure difference. g Oil Water PA 10 cm FIGURE P2.6.7 PASee Answer
Q17:2.6.5 WP The closed tank of Fig. P.2.6.5 is filled with water and is 5-ft long. The pressure gage on the tank reads 7 psi. Determine: (a) the height, h, in the open water column, (b) the gage pressure acting on the bottom tank surface AB, and (c) the absolute pressure of the air in the top of the tank if the local atmospheric pressure is 14.7 psia. T 2 ft 2 ft 1 Air A 7 psi Water B Open hSee Answer
Q18:2. This dome (hemisphere) is located below the water surface as shown. Determine the magnitude and sign of the force components needed to hold the dome in place and the line of action of the horizontal component of force. Here, y₁ = 1 m and y₂ = 2 m. Assume T = 10°C. Water Hemi- 2 spherical dome Atmospheric pressureSee Answer
Q19:3. Consider a porous medium composed of continuous, straight, parallel flow channels, whose cross-sectional area varies in a quasi-periodic manner (serial type non-uniformities). See Figure 2. Assume that the flow channels are all cylindrical in shape and that each channel is composed of segments of capillaries of two diameters, d, and d₂. Let N be the number of channels per unit cross-sectional area and L be the macroscopic length of the medium. Let L, and L2 be the total lengths of segments of sizes di and d2, respectively, in a channel (L, + L2 =L). (a) Develop a functional form of the intrinsic permeability of this medium. (b) Compare your result in part (a) to that predicted by assuming that the medium is composed of uniform parallel channels having the same mean hydraulic diameter as the system described above (Carman-Kozeny assumption). (c) To force the Carman-Kozeny model result to agree with that in part (a), what must you assume about the tortuousity of the medium depicted in Figure 2? Explain. (d) Extra Credit (10 points) - On page 259 of Dullien (1992), he presents an expression (eq. 3.3.10) which relates the permeabilities you computed in parts (a) and (b) above: k=kcx (1+y}{1+yx)/(1+yx)(1+y/x*), where x = d/d, and y=Ly/LI. Does his expression agree with your results? Show all work. L2 Li Figure 2 d₂See Answer
Q20:Problem 3. A fan is to be selected to ventilate a bathroom whose dimensions are 2 m x 3 mx 3 m. The air velocity is not to exceed 7 m/s to minimize vibration and noise. The combined efficiency of the fan-motor unit to be used can be taken to be 50 percent. If the fan is to replace the entire volume of air in 15 min, determine (a) the wattage of the fan-motor unit to be purchased, (b) the diameter of the fan casing (assume a round duct), and (c) the pressure difference across the fan. Take the air density to be 1.25 kg/m³ and disregard the effect of the kinetic energy correction factors. Air 7 m/s Exhaust fanSee Answer

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