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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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**Q1:**An airstream of speed 160 m/s and temperature 3000 K travels on the inside of a 30 cm I.D. steel tube whose wall thickness is 2.5 mm. On the outside of the tube, water coolant flows coaxially in an annular space 6.1 mm thick. The coolant velocity is 10 m/s, and it has a local temperature of 15°C. Both flows are approximately fully developed. The pressure of the airstream is around 140 kPa. Estimate the maximum wall temperature of the tube.See Answer**Q2:**An ideal gas undergoes a process between two specified temperatures, first at constant pressure and then at constant volume. For which case will the ideal gas experience a larger entropy change? Explain.See Answer**Q3:**A rigid vessel is filled with a fluid from a source whose properties remain constant. How does the entropy of the surroundings change if the vessel is filled such that the specific entropy of the vessel contents remains constant?See Answer**Q4:**Consider the object shown to the right, where: the total pressure force acting on the top is 7.6 N; the total pressure force on the bottom is 12.6 N; the total shear force on the top is 3.6 N, and the total shear force on the bottom is 3.4 N. The angle is 13 degrees.What is the total Drag on the object (in N)? See Answer**Q5:**Using the van der Waals equation of state, compute for Benzene the difference in molar enthalpy between an initial state at 700 K and 2,015 mol/m3 and a final state at 848K and3,850 mol/m3. Provide your answer in kJ/mol to the nearest 0.1 kJ/mol. Use the polynomial specific heat.See Answer**Q6:**Figure 1 below shows an early attempt to design, manufacture, and test a Direct Bloodoxygenator. Air, or O2 enriched air, was flown inside a "plastic bag" while blood was released atthe top of the oxygenator to slowly flow along the plastic bag's walls downward under theinfluence of gravity. Blood and Air were in direct contact, thus supporting a very efficient masstransport of O2 from Air to blood and transport of CO2 from blood to Air. Later, in the mid 20thcentury, scientists and engineers replaced these bags with gas permeable membranes, whichfacilitated gas transport between blood and Air. Nevertheless, the mass transport coefficient inmembrane-supported devices was lower than in the Direct Blood oxygenator. Consider isothermal, steady, unidirectional laminar flow of Blood down the wall of the direct contact oxygenator as illustrated in Figure 2a. The thin film of blood of approximate thickness8 = 165 [um] is flowing due to gravity only. The Shear Stress - Shear Rate data for blood at 25°C is presented in Figure 2b. a) (30 points) Using the data presented in Figure 2b determine the coefficients of the Shear Rate - Shear Stress relationship for Blood. b) (10 points) Apply the continuity equation for this application. What is the conclusion? c) (30 points) Develop a mathematical model [differential equation(s) + boundary conditions]that will represent the flow of Blood in the film along the walls of the plastic bag. Start from the conservation of momentum equations (Navier-Stokes) and show your work for the simplification. d) (50 points) Solve the mathematical model developed in (c) and obtain an algebraic expression that will represent the velocity profile u,(y) of Blood. e) (30 points) Develop the expression for the volumetric flow rate (Q) of blood in the Direct Blood oxygenator. Determine the volumetric flow rate of blood in Q(=)mL/min] if the width of the bag is W = 1.25 [m]. f) (10 points) Make a graph u (y) versus y; use Excel. g) (30 points) If the exponent 'n' in the solutions obtained in parts (d) and (e) is set to n =1,(and n= u) do your solutions reduce to i) velocity profile and ii) volumetric flow rate that could be obtained for a Newtonian fluid. Check and show all your work. Assumptions: The flow is assumed to be fully developed, isothermal, unidirectional and laminar. Momentum transfer between Blood and Air is negligible. One could assume that bloodди,is a non-Newtonian Power-Law fluid: T, =-nдуAlso, ignore entrance and exit effects of Blood flow. State any additional assumption. \begin{aligned} &\text { Momentum equation in } x \text { direction: }\\ &\rho\left[\frac{\partial u_{x}}{\partial t}+u_{x} \frac{\partial u_{x}}{\partial x}+u_{y} \frac{\partial u_{x}}{\partial y}+u_{z} \frac{\partial u_{x}}{\partial z}\right]=-\left[\frac{\partial \tau_{x x}}{\partial x}+\frac{\partial \tau_{x y}}{\partial y}+\frac{\partial \tau_{x z}}{\partial z}\right]+\rho g_{x} \end{aligned} \begin{aligned} &\text { Momentum equation in } y \text { direction: }\\ &\rho\left[\frac{\partial u_{y}}{\partial t}+u_{x} \frac{\partial u_{y}}{\partial x}+u_{y} \frac{\partial u_{y}}{\partial y}+u_{z} \frac{\partial u_{y}}{\partial z}\right]=-\left[\frac{\partial \tau_{y x}}{\partial x}+\frac{\partial \tau_{y y}}{\partial y}+\frac{\partial \tau_{y z}}{\partial z}\right]+\rho g_{y} \end{aligned} \begin{aligned} &\text { Momentum equation in z direction: }\\ &\rho\left[\frac{\partial u_{z}}{\partial t}+u_{x} \frac{\partial u_{z}}{\partial x}+u_{y} \frac{\partial u_{z}}{\partial y}+u_{z} \frac{\partial u_{z}}{\partial z}\right]=-\left[\frac{\partial \tau_{z x}}{\partial x}+\frac{\partial \tau_{z y}}{\partial y}+\frac{\partial \tau_{z z}}{\partial z}\right]+\rho g_{z} \end{aligned}See Answer**Q7:**Problem 1: We saw the demonstration of the upside down cup in class today. For the card to maintain contact with the glass, the forces acting up must be greater than the forces acting down. Calculate the maximum pressure at the top of the cup in a 0.5 cm gap at the top. The cup is filled with a volume of 450 cm³, assuming an atmospheric pressure of 101 kPa, and dimensions of the card of 6 cm x 4 cm.Assume a cylindrical glass with a diameter of 3.4 cm and the density of water is 1.0g/cm³. Don't be afraid if the number is not what you expect, but explain what it means.See Answer**Q8:**Air at 20 °C and 1 atm flows past a smooth flat plate at Uoo =20 m/s (below figure). A pitot stagnation tube, placed 1.2 mm from the wall, develops a water (Pu =998 kg/m) manometer head h = 20.04 mm. Assume the transition for this plate occurs at Re-106. Take the density and dynamic viscosity of air at 20 °C and 1 atm, as pa =1.205 kg/m and u = 1.81 x 10 kg/(m s). i) Calculate the velocity which is measured by the pitot tube. iii) Check to see if the flow is laminar i) Use this information with the Blasius solution to estimate the position x of the pitot tube.See Answer**Q9:**(a) State Newton's law of viscosity and define briefly the variables it relates to one[3 marks]another. (c) A 3-stage ultrafiltration (UF) plant is to be used to recover and concentrate an enzyme in wash water from a textile plant. The inlet flow rate is 5 m3 h-1 and the overall volume concentration factor (VCF) is 9.1. The VCF in stage 1 is 1.65; the membrane area in each stage is 20 m2. The flux in stage 2 is 77.1 L m-2 h-1(LMH). Use this information to calculate: (i)The retentate and permeate flow rate from each stage. (ii)The VCF and flux in each stage, and the effective average flux for thesystem as a whole. (b) Combine the equation for the shear stress at a pipe wall with the expression for the friction factor for laminar flow,to provide the following expression for the viscosity of a Newtonian fluid in laminar flow through a pipe of circular cross section: \mu=\frac{h \rho g d^{2}}{128 L} \frac{\pi d^{2}}{Q}, \text { where the symbols have their usual meanings. }See Answer**Q10:**Problem 2: Calculate the change in height of a fluid in a manometer when it is connected to a gas vessel with internal pressure 230 kPa if the manometer is filled with: (a) water, (1.0 g/cm³); (b) a liquid metal alloy (6.5 g/cm³), or (c) liquid mercury(13.6 g/cm³). Assume atmospheric pressure is equivalent to 101 kPa. (d) can you think of a good reason why manometers were filled with mercury rather than other fluids?See Answer**Q11:**Consider the truss structure shown with the following properties: A = 3 x 102 m“ E = 70 GPa 1. Find the element stiffness matrix for each truss 2. Put the element stiffness matrices in global coordinates and find the global equilibriumequation 3. Calculate the displacements at each node. 4. Calculate the reactions at each node. 5. Calculate the internal forces within each bar See Answer**Q12:**Consider a Newtonian fluid between two fixed wide, parallel plates, shown in the figure below,the velocity distribution for the fluid flow is given by: u=\frac{3 V}{2}\left[1-\left(\frac{y}{h}\right)^{2}\right] where V is the mean velocity. The fluid has a viscosity of 1.91 Pa.s, Also V = 0.6 m/s and h =0.5 cm.See Answer**Q13:**7-135E A frictionless piston-cylinder device contains saturated liquid water at 40-psia pressure. Now 600 Btu of heat is transferred to water from a source at 1000°F,and part of the liquid vaporizes at constant pressure. Determine the total entropy generated during this process, in Btu/R.See Answer**Q14:**An adiabatic diffuser at the inlet of a jet engine increases the pressure of the air that enters the diffuser at 11 psia and 30°F to 20 Dsia. What will the air velocity at the diffuser exit be if the diffuser isentropic efficiency, defined as the ratio of the actual kinetic energy change to diffuser inlet velocity is 1200/ ft/s See Answer**Q15:**7-127 An adiabatic steady-flow device compresses argon at 200 kPa and 27 C to 2 MPa. If the argon leaves this compressor at 550°C, what is the isentropic efficiency of the compressor?See Answer**Q16:**Ten grams of computer chips with a specific heat of 0.3 kJ/kg K are initially at 20°C. These chips are cooled by placement in 5 grams of saturated liquid R-134a at -40°C. Presuming that the pressure remains constant while the chips are being cooled, determine the entropy change of (a) the chips, (b) the R-134a, and (c) the entire system. Is this process possible? Why?See Answer**Q17:**An approximation for the boundary-layer shape in Figs.1.5b and P1.51 is the formula u(y) \approx U \sin \left(\frac{\pi y}{2 \delta}\right), \quad 0 \leq y \leq \delta where U is the stream velocity far from the wall and d is the boundary layer thickness, as in Fig. P1.51. If the fluid is helium at 20°C and 1 atm, and if U = 10.8 m/s and o = 3 mm,use the formula to (a) estimate the wall shear stress T in Pa, and (b) find the position in the boundary layer where Tis one-half of Tw. See Answer**Q18:**2 gallons per minute of water flows through a 0.5" diameter pipe. Assume the flow remains laminar What is the friction factor and pressure drop over 1 foot of pipe? b. Repeat part (a) for a square pipe with an equivalent hydraulic diameter.See Answer**Q19:**3 In Fig. 1.7, if the fluid is glycerin at 20°C and the width between plates is 6 mm, what shear stress (in Pa) is required to move the upper plate at 5.5 m/s? What is the Reynolds number if L is taken to be the distance between plates?See Answer**Q20:**Glycerin at 20°C fills the space between a hollow sleeve of diameter 12 cm and a fixed coaxial solid rod of diameter11.8 cm. The outer sleeve is rotated at 120 rev/min.Assuming no temperature change, estimate the torque required, in N m per meter of rod length, to hold the inner rod fixed.See Answer

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