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 24.4 m 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 24.4 m elevation while the free surface at the source tank is at 21.3 m elevation.

Answer 1

To find the flow rate in the pipeline, we can use Bernoulli's equation which states that the total head at any point in a fluid system is constant. By considering the head loss at both the suction and discharge sides and using the elevation difference between the source and discharge tanks, we can solve for the flow rate.

Step-by-step explanation:

To find the flow rate in the pipeline, we need to use Bernoulli's equation which states that the total head at any point in a fluid system is constant. The total head is the sum of the pressure head (P/ρg), velocity head (v^2/2g), and elevation head (z). At the suction side, the head loss is 5 times its velocity head, and at the discharge side, the head loss is 12 times its velocity head.

Let's assume the flow rate in the pipeline is Q. According to Bernoulli's equation, the total head at the suction side is 24.4 m + 5Q2/2g, and the total head at the discharge side is 12Q2/2g. Since the source and discharge tanks are exposed to the atmosphere, the elevation heads at both ends are the same, which is 24.4 m - 21.3 m. Equating the total heads at both ends and solving the equation will give us the flow rate (Q).