UBC CHBE 251 - Fluid Mechanics - Problems From Past Finals

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PROBLEMS FROM PAST FINAL EXAMS

CHBE 251 – Transport Phenomena I

INSTRUCTOR:

SAVVAS G HATZIKIRIAKOS

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PROBLEM (FINAL 2007) ( 25% )

The small turbine in the Figure below extracts 400 W of power from the water flow. Both

pipes are wrought iron. Compute the flow rate Q in m3/hr. (20%)

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PROBLEM (FINAL 2007) (25%)

The pressure drop per unit length Δp/L in smooth pipe flow is known to be a function of only

of average velocity V, diameter D, and fluid properties ρ and μ. The following data were

obtained for flow of water at 20 0C in an 8-cm-diameter pipe 50 m long: Q, m3/s

0.005

0.01

0.015

0.020

Δp, Pa

5,800

20,300

42,100

70,800

(a) Perform a dimensional analysis to identify the dimensionless groups which describe the

process (Do not select μ as repeating variable) (10%).

(b) Use the above given data to estimate the pressure drop for flow of kerosene at 20 0C in a

smooth pipe of diameter 5 cm and length 200 m if the flow rate is 60 m3/h. If needed you may

use the log-log graph paper provided in the next page. Do not forget to detach this page and

include it with your exam (15%).

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PROBLEM (FINAL 2008) ( 30% )

Cooling water ( 3/980 mkg , 23 /.10 msN ) is pumped from a reservoir to rock drills on a

construction job using the pipe system shown in the Figure below . The flow rate must be

0.03785 m3/s.

(a) Calculate the minimum pressure needed at the pump outlet.

(b). Estimate the required power input if the pump efficiency is 70 percent.

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PROBLEM (FINAL 2008) ( 20% )

A fluid flows along the x axis with a velocity given by V=(x/t)i, where x is in feet, t in

seconds and i is the unit vector in the x direction.

(a) Plot the speed for 0 x 10 ft and t = 3 s (Use the graph paper provided on the page

4).

(b) Plot the speed for x = 5 ft and 2 t 4 s (Use the graph paper provided on page 4).

(c) Determine the local and convective acceleration.

(d) Show that the acceleration of any fluid particle in the flow is zero.

(e) Explain physically how the velocity of a particle in this unsteady flow remains

constant throughout its motion.

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PROBLEM (FINAL 1995) (20%)

Answer briefly all the following questions.

a. Consider a Newtonian and a pseudoplastic fluid which have the same viscosity at very small

shear rates. Which of the two fluids flows faster in a pipe of constant diameter under the

action of the same pressure gradient and why? (4%)

b. Is it true that the continuity equation is valid for both viscous and inviscid, Newtonian and

non-Newtonian, compressible and incompressible, laminar and turbulent flow? If so, are there

any limitations on this equation? (4%)

c. For axial flow through a circular tube, the Reynolds number for transition to turbulence is

approximately 2,300 based upon the diameter, D and average velocity. If D=5 cm, calculate

and compare the volumetric flow rates at the point of transition for flow of water and kerosine

at 20oC. (4%)

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d. Fill a glass approximately 80% with water , and add a large ice cube. Mark the water

level. The ice cube, having SG=0.9, sticks up out of the water. Let the ice cube melt with

negligible evaporation from the water surface. Will the water level be higher, lower than,

or the same as before? (4%)

e. Suppose that it is desired to estimate the volumetric flow rate, Q in a pipe by measuring the

axial velocity uz(r) at specific points. For cost reasons only three measuring points are to be

used. What are the best radii selections for these three points? (4%)

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PROBLEM 1 - April 2009 - (10%)

A 0.15 m - diameter piston is located within a cylinder which is connected to a 1.25 cm –

diameter inclined tube monomer as shown in Figure. The fluid in the cylinder and the

manometer is oil (specific weight = 10 kN/m3). When a weight, W, is placed on the top of the

cylinder, the fluid level in the manometer tube rises from point (1) to (2). How heavy is the

weight in kg?

PROBLEM 2 - April 2009 - ( 20% ) Water flows from a large tank through a large pipe that splits into two smaller pipes as shown

in Figure. If viscous effects are negligible, determine the volumetric flow rate from the tank

(15%) and the pressure at point (1) (5%).

PROBLEM 3 - April 2009 - (20%)

A model test of a tractor-trailer rig is performed in a wind tunnel. The drag force, FD, is found

to depend on the frontal area, A, wind speed, V, air density, , and air viscosity, . The model

scale is 1:4; frontal area of the model is A=0.625 m2. Obtain a set of dimensionless parameters

suitable to characterize the model test results (15%). State the conditions required to obtain

dynamic similarity between model and prototype flows. When tested at wind speed V=89.6

m/s, in standard air, the measured drag force on the model was FD=2.46 kN. Assuming

dynamic similarity, estimate the aerodynamic drag force on the full-scale vehicle at V=22.4

m/s (5%).

PROBLEM 4 - April 2009 - (30%)

A large reservoir supplies water for a

community. A portion of the water

supply system is shown in Figure.

Water is pumped from the reservoir to

a large storage tank before being sent

on to the water treatment facility. The system is designed to provide 1.31 m3/s of water of 20oC.

From B to C the system consists of a square-edged entrance, 760 m of pipe, three gate valves, four

45o elbows, and two 90o elbows. Gage pressure at C is 197 kPa. The system between F and G

contains 760 m of pipe, two gate valves, and four 90o elbows. All pipe is 508 mm diameter, cast

iron. Calculate:

(a). The average velocity of water in the pipe. (5%)

(b). The gage pressure at section F. (15%)

(c). The power input to the pump (its efficiency is 80 percent). (10%)

PROBLEM 5 - April 2009 - (20%)

Consider fully developed laminar flow in the space between two parallel plates placed at a

distance 2h under the influence of a pressure gradient dxdp / which is taken to be known (see

Figure ). The lower plate is stationary and the upper plate moves in the x direction with speed

V. Note that this problem has been solved in class and the velocity profile can be found in the

notes as a superposition of two flows.

(a). Obtain a general expression for the velocity V so that the shear stress on the moving plate

to be zero. (15%)

(b). Sketch the velocity profile and shear stress for this case and explain. (5%)