Fluid Mechanics

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.

4) An oil with a specific gravity of 0.833 and a viscosity of 3.3 cP is pumped from an open tank to a closed, pressurized tank maintained at 40 psig. The oil is pumped at a rate of 0.15 ft3/sec through 70 ft of 4-in, schedule-40 commercial steel pipe to the pump. The suction-side piping system contains a wide-open gate valve and a 90° elbow. On the discharge side of the pump, there is 300 ft of 3-in, schedule-40 commercial steel pipe. The discharge-side piping system contains two 90° elbows and a half-open globe valve, all after the pump. The liquid level in the open tank is 60 ft above the liquid level in the pressurized tank. The pump efficiency is 75%. Calculate the power required for the pump in hP.

7) Ethanol (u=1.2 x 10-³ Pa*s, p= 788 kg/m³ at 20°C) flows from tank A to tank B via a galvanized iron circular pipe with a diameter of 7.5 cm. The pipeline is 16m long and contains two 90° elbows. Tank A is 2 m higher than tank B. Both tanks are open to the atmosphere. Determine the volumetric flow rate (m³/s) of ethanol.

1. A pressurized tank contains oil (s = 0.9) and has a triangular gate of negligible weight, as illustrated below. Compute the magnitude of force F so that the gate remains closed as shown. Note: Since the gate is non-rectangular, you should perform the above problem using the general approach, however you cannot use F = yh₂A nor y₂ = Yc+Ixx.c/Ayc because these equations were derived while taking pressure equal to zero at the liquid surface. Meanwhile in this problem pressure is not equal to zero at the surface of the oil. Thus, looking back at the week 8/part 1 lecture notes posted on Canvas, you should re-derive the expressions for F and y, valid for non-zero pressure at the surface.

Question 2 The Figure below shows a nozzle through which there is steady flow of water. The outlet of the nozzle is open to the atmosphere. By using the data in the next paragraph, you must determine the horizontal component of force required to keep the nozzle in place. Please, comment on the result.

Question 3 Arectangulargate (shown in the figure below) is located at the end of a rectangular passage that is connected to a lake filled with an unknown liquid. The gate is hinged at the bottom and held closed by a horizontal force FH, applied to the centre of the gate. On the surface of the lake is stationing a river barge whose cross section is approximately rectangular. Its draft (depth of submergence) is hB. Determine the maximum water depth, h, above the centre of the gate that can exist without the gate opening. Is the answer the same if the gate is hinged at the top?

An amazing number of commercial and laboratory devices have been developed to measure fluid viscosity, as described in Ref. 29 and 49. Consider a concentric shaft, fixed axially and rotated inside the sleeve. Let the inner and outer cylinders have radii ri and ro, respectively, with total sleeve length L. Let the rotational rate be 2 (rad/s) and the applied torque be M. Using these parameters, derive a theoretical relation for the viscosity of the fluid between the cylinders.

Derive an expression for the capillary height change h for a fluid of surface tension Y and contact angle between two vertical parallel plates a distance W apart, as in Fig. P1.70. What will h be for water at 20° C if W=0.5 mm?

(a) Prove that both of these formulas are dimensionally homogeneous. (b) Suppose that a 2.5 mm diameter aluminum sphere (density 2700 kg/m³) falls in an oil of density 875 kg/m³. If the time to fall 50 cm is 32 s. estimate the oil viscosity and verify that the inequality is valid.

Pipelines are cleaned by pushing through them a close-fitting cylinder called a pig. The name comes from the squealing noise it makes sliding along. Ref. 50 describes a new non-toxic pig. driven by compressed air, for cleaning cosmetic and beverage pipes. Suppose the pig diameter is 5-15/16 in and its length 26 in. It cleans a 6-in-diameter pipe at a speed of 1.2 m/s. If the clearance is filled with glycerin at 20°C, what pressure difference, in pascals, is needed to drive the pig? Assume a linear velocity profile in the oil and neglect air drag.