Fluid Mechanics: Tutorials - Unit 2

1. An oil of 8 Poise and specific gravity 0.9 is flowing through a horizontal pipe of 50 mm diameter. If the pressure drop in 100 m length of the pipe is 2000 KN/m², determine (i) Rate of flow of oil (ii) Center line velocity (iii) Total frictional drag over 100 m length of pipe (iv) Power required to maintain the flow (v) Velocity gradient at the pipe wall (vi) Velocity and shear stress at 10 mm from the wall.

[3.83 x 10^-3 m³/s; 3.9 m/s; 3.93 KN; 7.65 KW; 312 S^-1; 2.5 m/s; 150 N/m²]

2. An oil of viscosity 1 Poise and relative density 0.9 is flowing through a circular pipe of diameter 50 mm and 300 mm length, the rate of flow of liquid is 0.0035 m³/s. Find the pressure drop and shear stress at the wall. [684.3 KN/m²; 28.5 N/m²]

3. In a pipe of 300 mm diameter and 800 m length, an oil of specific gravity 0.8 is flowing at the rate of 0.45 m³/s. Find the head lost due to friction and power required to maintain the flow. Take kinematic viscosity of oil as 0.3 x 10^-4 m²/s. [109.72 m; 387.48 KW]

4. A horizontal pipe 150 mm in diameter is joined by sudden enlargement to a 225 mm diameter pipe. Water is flowing through it at the rate of 0.05 m³/s. Find (i) Loss of head due to sudden expansion (ii) Pressure differences in two pipes (iii) Change in pressure if the change is gradual without any loss. [0.1256 m; 0.202 m; 0.327 m] {Note: Power lost due to expansion}

5. A horizontal pipe carries water at the rate of 0.04 m³/s. Its diameter which is 300 mm reduces abruptly to 150 mm. Calculate the pressure loss across the contraction. Take the co-efficient of contraction as 0.62. [3.35 KN/m²]

6. Two reservoirs with a difference in water surface elevation of 10 m are connected by a pipeline ABC which consists of two pipes AB and BC joined in series. Pipe AB is 10 cm in diameter, 20 m long and has a value of f= 0.02. Pipe BC is of 16 cm diameter, 25 m long and f= 0.018. The junctions with the reservoirs and between the pipes are abrupt. Find (i) Discharge including all losses (ii) Discharge neglecting minor losses (iii) What difference in reservoir elevation is necessary to have a discharge of 15L/S, if all losses are included? [43.8 L/S; 1.171 m]

7. Three pipes are connected in parallel between two reservoirs A and B. The details of the pipes are

Pipe	Diameter (cm)	Length (m)	f
1	10	1000	0.022
2	15	800	0.018
3	12	950	0.020

If the difference in the water level elevations of the two reservoirs is 12 m; estimate the discharge in each pipe. [0.0081; 0.0277; 0.0138 m³/s]

8. Pipeline carrying water has a diameter of 0.5 m and is 2 km long. To increase the delivery another pipeline of same diameter is introduced parallel to the first pipe in the second half of its length. Find the increase in discharge if the total head loss in both the cases is 15 m. Assume f= 0.02 for all the pipes. [0.3766m³/s; 0.4763m³/s; 26.48%]

9. A compound piping system consists of 1800 m of 50 cm, 1200 m of 40 cm and 600 m of 30 cm diameter pipes of the same material connected in series. (i) What is the equivalent length of a 40 cm pipe of the same material? (ii) What is the equivalent size of the pipe 3600 m long? (iii) If the three pipes are in parallel, what is the equivalent length of a 50 cm pipe? [4318.22 m; 38.57 cm; 377.34 m]

10. A horizontal pipe 40 m long is connected to water tank at one end and discharge freely into atmosphere at the other end. For the first 25 m of its length from the tank, the pipe is 150 mm diameter and it’s suddenly enlarged to 300 mm. The height of the water level in the tank is 8 m above the centre of the pipe. Including all losses find (i) Q, (ii) HEL, TEL f=0.01