THE UNIVERSITY OF WESTERN ONTARIO



The University of Western Ontario

Faculty of Engineering

Department of Mechanical & Materials Engineering

MME 273b – Fluid Mechanics 1- Example of a previous Quiz 3

Closed Book 1 hour 30 minutes

AIDS: One Crib Sheet (8 1/2" x 11") both sides (no photocopies), Calculator,

Handouts of valve and pipe flow loss coefficients (2 sheets)

In the pipe system below (not drawn to scale), water of density 1000 kg/m3 and dynamic viscosity 0.001 kg/ms flows from a large pressurised (Ps) reservoir through a system composed of galvanised iron pipework and a fully open flanged swing check valve. The network begins with 100 mm diameter pipe from the reservoir and then, after a sudden contraction, there is a 5 m length of 20 mm diameter pipe. This is followed by a sudden expansion back to 100 mm diameter pipe and, finally the water exits the network at point C as a free jet through a 50mm diameter orifice with a discharge coefficient (Cd) of 0.8. At the exit, a pitot tube is used to measure the free jet stagnation pressure. The tube is connected to a manometer that is inclined at an angle of 3o to the horizontal and is open to the atmosphere at the top. The tube, filled with oil of specific gravity SG = 0.8, gives a scale reading along the manometer of L = 1.2 mm. Calculate:

a) The volume flow rate through the pipe network. [Answer = 4.93 x 10-5 m3/s)

b) The absolute surface pressure within the reservoir (Ps) required in order to achieve this flow rate [68.12kPa].

c) The pressure difference between the points A and B in terms of the liquid column height if a U-tube manometer is connected between points A and B. The manometer fluid has a specific gravity of SG = 1.2.

[Answer = 86.81 mm]

The entrance loss coefficient to the pipework from the reservoir may be taken as Ke = 0.5 and the pressure at the exit may be taken as atmospheric (Patm = 101.3 kPa).

NOTES: To aid your study of this trial question, first remember that you need to know the flow velocity in order to compute the losses. The pitot tube at the end allows you to do this. The flow coming out of the pipe hits the end of the pitot tube and so it measures the stagnation (total) pressure there. The other end of the pitot tube measures the atmospheric (static pressure) and so the difference is the dynamic pressure, ½(U2 which the manometer in the pitot tube measures as a vertical height of liquid. From the velocity, U, you can compute the discharge Q (m3/s) remembering to use the discharge coefficient. You know the open end of the pipe at C is at atmospheric pressure so you use the modified Bernoulli equation to work back through the losses to find the pressure in the reservoir. Finally, since you can apply the modified Bernoulli equation between any two points, you apply it between A and B to find the manometer height difference.

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