Basics and flow through pipes

1. Derive continuity equation from basic principles. 2. Derive Euler's equation of motion for flow along a stream line. What are the assumptions involved? 3. What do you mean by displacement thickness, momentum thickness and energy thickness? 4. Two pipes of 15 cm and 30 cm diameters are laid in parallel to pass a total discharge of 100 liters per second. Each pipe is 250 m long. Determine discharge through each pipe. Now these pipes are connected in series to connect two tanks 500 m apart, to carry same total discharge. Determine water level difference between the tanks. Neglect minor losses in both cases, f = 0.02 both pipes. 5. Derive an expression for the velocity distribution for viscous flow through a circular pipe. 6. Three pipes of 400 mm, 350 mm and 300 mm diameter are connected in series between two reservoirs. With a difference in level of 12 m. Friction factor is 0.024, 0.021 and 0.019 respectively. The lengths are 200 m, 300 m and 250 m. Determine flow rate neglecting minor losses.