Mex 3212

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Q1 (a) Define density and relative density. What are the different units of measurement of density? (b) Explain how the relative density of a liquid is found using specific gravity bottle. (c) A metal casting is expected to have a specific gravity of 7.5. Due to entrap air bubbles the actual specific gravity was found to be 6.5. What percentage of the casting filled with air? (Neglect the mass of air in calculation). Q2 (a) Write down the relationship for the dynamic viscosity of fluid in terms of velocity gradient and the shear stress and name its terms with their SI units of measurement. (b) Fig Q2 below shows a rotating disc viscometer, in which a disc of radius R rotates at an angular speed of . The distances from the rotating disc surface to the stationary housing is h in each side.

Show that the torque T, required is given by the following formula: ������������������ 4 ������ ℎ Hint: Consider a small annulus at a distance r from the center and write down the forces on this area due to fluid shear and then the torque. Integrate from r = 0 to r = R to obtain the total toque. ������ =

Q3 (a) What is meant by center of pressure when a body is immersed in water?

(b) When a rectangular plate is submerged in a fluid, show that magnitude of fluid thrust (F) acting on the plate is given by: F = Area of the plate X Fluid pressure at the centre of gravity of the plate

(c) A rectangular shape gate AB of 2m height and 1m wide is used to close the opening of a water tank as shown in Fig.Q3. The gate is hinged at A.

Fig. Q3 Find (i) (ii) (iii)

Fluid thrust (F) acting on the gate. Distance to point of action of the force F from the water surface Force that should be applied at the lower edge of the gate to prevent it opening.

Q4

(a) Write down Bernoulli’s equation for incompressible fluid flow, and name the variables with their SI units of measurement. (b) A 2kW pump is used to lift water from a reservoir to a location, 20m above it. The total...
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