Q1. (a) A closed tank shown in figure contains a layer of oil lying above water. Three pressure gauges are fitted as shown. If the pressure of the air in the tank is 22.3kN/m2 and gauge A reads 34.1kN/m2, calculate:
(i) the specific gravity of the oil and
(ii) the pressure read by gauge B.
(b) Two tanks, shown in figure, are connected by a mercury manometer. Tank A contains water and Tank B contains carbon tetrachloride with a specific gravity of 1.6. If the mercury levels in the manometers are 140mm different, then calculate the depth of carbon tetrachloride in tank B.
Q2. (a) Define "absolute pressure" and "gauge pressure" and explain the relationship between the two.
(b) Two tanks, one containing water and the other seawater (density 1025kg/m3) have piezometers connected to them and are connected by a differential mercury manometer (SG = 13.6) as indicated in Figure. The gauge pressure in tank A is 9.38 kPa. Calculate the absolute pressure in tank A if atmospheric pressure is 758mm of mercury.
(c) The reading on the mercury manometer connecting the tanks is 44mm. Calculate the head readings, zA and zB, given by the manometers.
Q3. (a) The head of water above a sharp crested weir is 2m and the dam itself is 17m high (see Figure). Calculate the resultant force per metre width, acting on the whole face of the dam, and the depth to the centre of pressure.
(b) A water level control device in the vertical side of a tank consists of an equilateral triangular flap of side 0.8 m. One edge of the flap is horizontal and the apex points downwards as shown in Figure Q5 (b). The flap is pivoted about a horizontal axis on the plane of the tank side. Determine the position of this axis so that the water level inside the tank is kept constant at 1.2 m above the top edge of the flap.
(c) The flap gate described in part (b) is replaced with a square gate of sides 0.8m as shown in Figure Q5 (c). Determine the new position of the axis so that the water level inside the tank is maintained constant at 1.2 m above the top edge of the flap.
Q4. (a) The flow of water from a tank is controlled by a 600mm square flap gate. The gate is held closed against a 1.3m depth of water by a weight attached to the back of the gate as shown in Figure Q2-b. Calculate the total pressure force acting on the gate and the depth to the centre of pressure.
(b) The weight on the back of the gate, of (a) above, consists of a full tank of water. The tank is 400mm x 600mm x 1200mm in size and is welded by one of its square sides to the gate as indicated in the diagram. If the water in the tank is drained off at 30 I/min how long will it be before the gate opens. Ignore the weight of the gate itself, the empty weight of the tank and friction in the hinge.
Q5. (a) With the aid of simple diagrams define what is meant by the terms:
(i) Centre of buoyancy
(ii) Metacentre
(iii) Metacentric height
(b) A pontoon floating in water is 20m long by 6m wide by 2m deep, has a mass of 150,000kg and its centre of gravity is at the geometric centre, lm above its base. Find, and indicate on a diagram, the position of the centre of buoyancy. Determine the metacentric height of the barge in water and show that it is stable.
(c) Determine the position of the centre of gravity of the pontoon when it is 'just stable' (i.e. it is in neutral equilibrium).
Q6. (a) A bridge floating in water as shown in Figure consists of pontoons 18m long by 8m wide by 4m deep. One of these pontoons is found to float to a depth of 2.4m in its unloaded state. Find the mass of the pontoon.
(b) A 20 tonne cargo is used to test the pontoon. The centre of gravity of the cargo is 1.3m above the floor of the pontoon. When it is positioned on the pontoon with its centre of gravity 2m horizontally from the centre line, as indicated in the diagram below, it is found that the angle of roll is 3.5°. Calculate and indicate on a diagram the position of the centre of gravity of the unloaded pontoon.
Q7. (a) With the aid of a clearly labelled sketch and stating any assumptions made, derive a formula for the actual flow rate through an orifice plate meter.
(b) Water flows through a horizontal orifice plate meter. The pipe is 22mm in diameter and the diameter of the orifice is 16mm. Determine the difference in piezometric head across the orifice plate meter when the actual flow through the orifice plate is 0.266 Vs and the coefficient of discharge is 0.65.
Q8. (a) Show, deriving any equations used and clearly stating any assumptions made, that the actual discharge of water from a V-notch weir is given by:
QA = (8/15)CD√(2g)tan(θ/2)H5/2
where θ is the angle of the notch, H is the head above the point of the notch and CD is the coefficient of discharge.
(b) If a sharp-crested V-notch discharges 1.08m3/s under a head of 0.72m, calculate the angle of the notch (to the nearest degree) assuming a coefficient of discharge of 0.6.
