Solution of Tutorial 5MI263 2013-14

1. A pipeline is 120 m long and 250 mm in diameter. At the outlet there is a nozzle 25 mm in diameter controlled by a shut-off valve. When the valve is fully open water issues as a jet with a velocity of 30 m S-I. Calculate the reaction of the jet.

If the valve can be closed in 0.2 s what will be the resulting rise in pressure at the valve required to bring the water in the pipe to rest in this time? Assume no change in density of the water and no expansion of the pipe.

2. A jet of water 50 mm in diameter with a velocity of 18 m S-I strikes a flat plate inclined at an angle of 25° to the axis of the jet. Determine the normal force exerted on the plate (a) when the plate is stationary, (b) when the plate is moving at 4.5 m S·I in the direction of the jet, and (c) determine the work done and the efficiency for case (b).

3. A lawn sprinkler consists of a horizontal tube with nozzles at each end normal to

the tube but inclined upward at 40° to the horizontal. A central bearing

incorporates the inlet for the water supply. The nozzles are of 3 mm diameter

and are at a distance of 12 cm from the central bearing. If the speed of rotation

of the tube is 120 rev min-I when the velocity of the jets relative to the nozzles is

17 m S-I, calculate (1I) the absolute velocity of the jets, (b) the torque required

to overcome the frictional resistance of the tube and bearing.

4. A liquid flows through a circular pipe 0.6 m in diameter. Measurements of

velocity taken at intervals along a diameter are:

Distance from the wall

m 0 0.05 0.1 0 . 2 0.3

V e l o c i t y m / s - 1 0 2 . 0 3.8 4 . 6 5.0

Distance from the wall

m 0.4 0 . 5 0.55 0 . 6

V e l o c i t y m / s - 1 4.5 3 . 7 1.6 0

Draw the velocity profile, calculate the mean velocity.

5. An orifice plate is to be used to measure the rate of air flow through a 2 m diameter duct. The mean velocity in the duct will not exceed ! 5 m S-I and a water tube m~nometer, having a maximum difference between water levels of 150 mm, is to be used. Assuming the coefficient of discharge to be 0.64, determine a suitable orifice diameter to make full use of the manometer range. Take the density of air as 1.2 kg/m3.

6. Water flows from a reservoir through a rectangular opening 2 m high and 1.2 m wide in the vertical face of a dam. Calculate the discharge in cubic metres per second when the free surface in the reservoir is 0.5 m above the top of the opening assuming a coefficient of discharge of 0.64. [8.16 m) s-l).