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Tutorial Sheet 7 The Bernoulli Equation1. A pipe of 150mm bore is delivering water at the rate of 7500dm3/min at a pressure of 820kN/m2. It connects by a gradually expanding pipe to a main of 300mm bore which runs 3m above it. Find the pressure in the 300mm main, neglecting losses due to friction.(814 kN/m2)

2. Water flows from a reservoir into a closed tank in which the pressure is 70 kN/m2 below atmospheric. If the water level in the reservoir is 6m above that in the tank, find the velocity of the water entering the tank, neglecting friction.

(16.05 m/s)

3. A pipe, whose axis is horizontal, is full of water in motion. At a section A the velocity of the water is 90m/min and the pressure is 138kN/m. If the pipe tapers gradually from 150mm diameter at A to 100mm diameter at B, determine the pressure of the water at B, assuming that there is no loss of energy. What must be the diameter of the pipe at B if the pressure there is reduced to 27.6kN/m2.(133 kN/m2; 47.6mm)

4. A vertical pipe carrying liquid of specific gravity 0.83 upwards from a pump contracts gradually from 105mm diameter to 35mm diameter over a length of 0.45m. A water U-tube is connected to two points 0.6 m apart in the two sections of the pipe and the head difference registered is 0.43m. The connecting pipes to the U-tube are filled with the liquid that is flowing. Find the rate of flow in dm3/min. Ignore energy losses.(76.4 dm3/min)

5. In a vertical pipe conveying water, pressure gauges are inserted at A and B where the diameters are 150mm and 75mm respectively. The point B is 2.4m below A and when the rate of flow down the pipe is 21dm3/s the pressure at B is 12kN/m2 greater than at A. Assuming that the losses in the pipe between A and B can be expressed as kV2/2g where V is the velocity at A, find the value of k. (1.375)6. The throat and full bore diameters of a venturi meter are 19mm and 57mm, respectively. Calculate the coefficient of discharge of the meter if the pressure at the full bore section is 172.5kN/m2 above that at the throat when the meter is passing 311dm3/min of water. The centreline of the meter is inclined to the horizontal, the throat section being 0.46m above the full bore section.(0.99)

7. A pitot-static tube placed in the centre of a 200mm pipeline conveying water has one orifice pointing upstream and the other perpendicular to it. If the pressure difference between the two orifices is 38mm of water when the discharge through the pipe is 22dm3/s, calculate the meter coefficient. Take the mean velocity in the pipe to be 0.83 of the central velocity.(0.97)

8. A closed tank partially filled with water discharges through an orifice of 12.5mm diameter and has a coefficient of discharge of 0.7. If air is pumped into the upper part of the tank, determine the pressure required to produce a discharge of 36dm3/min when the water surface is 0.9m above the outlet. (15.7 kN/m2)

9. Find the diameter of a circular orifice to discharge 15dm3/s under a head of 1.5m using a coefficient of discharge of 0.6. If the orifice is in a vertical plane and the jet falls 250mm in a horizontal distance of 1.2m from the vena contract, find the value of the coefficient of contraction.(76.6mm, 0.612)

10. Calculate the theoretical discharge through a vertical orifice 0.3m square in the side of a tank if the free surface of the liquid in the tank is 150mm above the top edge of the orifice. Compare this value with that obtained by multiplying the orifice area by the theoretical velocity at the centre.(0.216m3/s, 0.218m3/s)