(Solved): (a) Dimensionless numbers are always use in analysis of fluid mechanics. Define the following dime ...

(a) Dimensionless numbers are always use in analysis of fluid mechanics. Define the following dimensionless number in and explain their application in fluid mechanics and heat transfer problems. i. Reynold number \( (R e) \) ii. Mach number \( (M) \) iii. Prandtl number \( (\mathrm{Pr}) \) iv. Nusselt number \( (\mathrm{Nu}) \) (6 marks) (b) In the following figure, alcohol (s. \( g .=0.8) \) enters pipe 1 at \( 6 \mathrm{~m} / \mathrm{s} \) and water enters pipe 2 at \( 10 \mathrm{~m} / \mathrm{s} \). Assuming the mixture is ideal mixing of incompressible fluids, calculate the exit velocity and density of mixture at outlet 3. Pipe (1) and (2) are of diameters \( 30 \mathrm{~cm} \) and diameter of pipe (3) is \( 40 \mathrm{~cm} \) (6 marks) (c) A siphonic system as shown in below figure is designed to discharge liquid (s. \( g=0.84) \) from a reservoir into open air. If the velocity of flow in the pipe is \( v \mathrm{~m} / \mathrm{s} \), the frictional loss from Point 1 to Point 2 is \( 2.0 v^{2} / 2 \mathrm{~g} \) and frictional loss from Point 2 to Point 3 is \( 3.0 v^{2} / 2 g \), determine (8 marks) i. Flow rate in the siphon pipe ii. Pressure at Point 2