, November 2008
(a) Give the dimensions, S.I. units and C.G.S. units of the following fluid properties:
i. Specific weight
iii. relative density
iv. dynamic viscosity and
v. Kinematic viscosity
(b) Starting from their definitions, obtain the dimensions of the following derived quantities in MLT system
iii. Pressure and
iv. Surface tension
2. A rectangular door 1.8 m high and 0.9 m wide closes an opening in the vertical side of a tank which retains water on one side of it up to a depth of 1.8 m above the top edge of the door, the door is supported by two hinges placed 10 cm from the top and 10 cm from the bottom of one of the vertical sides and it is fastened by a bolt fixed at the centre of the other vertical side. Determine the force on each bolt and on the hinge.
3. (a) The velocity of a 3-D flow field is given by V = (y2+z2)i + (x2+z2)j + (x2+y2)k
Determine the acceleration components at a point (1,2,3)
(b) Derive the continuity equation for a 3-D fluid flow.
4. Gasoline which has a vapour pressure of 5.5 x 104 Pa (abs) and density ? = 680
kg/m3 flows through a constriction in a pipe where diameter is reduced from 20cm to 10 cm. The pressure in the 20 cm pipe just upstream of the constriction is 50 KPa. If the atmospheric pressure is 75 cm of mercury, calculate the maximum discharge that can be passed through this constriction without cavitation occurring.
5. (a) Differentiate between
i. Stream line body and bluff body
ii. Friction drag and pressure drag.
(b) A kite 60cm x 60cm weighing 2.943 N assumes an angle of 10o to the horizontal.
If the pull on the string is 29.43N when the wind is flowing at a speed of 40 km/hr. Find the corresponding coefficient of drag and lift. Density of air is given as 1.25 kg/m3.
6. (a) Describe Reynold’s experiment with a neat sketch. What are the outcomes of
(b) A crude oil of viscosity 0.97 poise and relative density 0.9 is flowing through
a horizontal circular pipe of diameter 10cm and of length 10m. Calculate the difference of pressure at the two ends of the pipe, if 100 kg of the oil is collected in a tank in 30 seconds.
7. The population of a city is 8X105 and it is to be supplied with water from a reservoir
6.4 km away. Water is to be supplied at the rate of 0.14m3 per head per day and half the supply is to be delivered in 8 hours. The full supply level of the reservoir is R.L 180.00. and its lowest water level is R.L.105.00. The delivery end of the main is at R.L 22.50 and the head required there is 12m. Find the diameter of the pipe. Take f= 0.04.
8. A rectangular channel 6 m wide carries 2.8 m3 per second at a depth of 0.9 m. What height of a broad crested rectangular weir must be installed to double the depth? Take coefficient of weir = 0.86.