Question

A pump is used to supply water through a pipeline 152 mm diameter at suction side and 102 mm diameter at discharge. Find the flow rate in the pipeline if the pump develops a head of 24.4m assuming the head loss at suction is 5 times its velocity head while the head loss at discharge is 12 times its velocity head. Both the source tank and the discharge tank is exposed to atmosphere. The free exit at discharge tank is at 24.4m elevation while the free surface at the source tank is at 21.3m elevation.

Answer 1

To find the flow rate in the pipeline, use the principle of continuity and the cross-sectional areas at the suction and discharge sides. Equate the flow rates to find the flow rate in the pipeline.

Step-by-step explanation:

To find the flow rate in the pipeline, we can use the principle of continuity. According to the continuity equation, the flow rate in a pipe is constant, so the flow rate at the suction side and discharge side should be the same.

Given that the diameter at the suction side is 152 mm and at the discharge side is 102 mm, we can calculate the respective cross-sectional areas. The area at the suction side is π(0.152/2)^2 and the area at the discharge side is π(0.102/2)^2.

Since the flow rate is constant, we can equate the cross-sectional areas and find the flow rate:

1. Area at suction side * Velocity at suction side = Area at discharge side * Velocity at discharge side
2. Flow rate at suction side = Flow rate at discharge side
3. π(0.152/2)^2 * Velocity at suction side = π(0.102/2)^2 * Velocity at discharge side
4. Cancelling out π, simplifying and solving for Velocity at discharge side will give us the flow rate in the pipeline.