Exciting Flow Rate Calculation in a Pipeline!

How can we determine the flow rate in the pipeline based on the given data?

What factors need to be considered to calculate the flow rate?

Calculating the Flow Rate in the Pipeline

To determine the flow rate in the pipeline, we need to use the principle of continuity and consider the cross-sectional areas at the suction and discharge sides of the pipeline. By equating the flow rates at both ends, we can find the flow rate in the pipeline.

Exciting news! We have an interesting problem to solve related to the flow rate in a pipeline. In this scenario, a pump is used to supply water through a pipeline that has a diameter of 152 mm at the suction side and 102 mm at the discharge side.

The pump develops a head of 24.4 meters, with the head loss at the suction side being 5 times its velocity head and the head loss at the discharge side being 12 times its velocity head. The source tank and the discharge tank are both exposed to the atmosphere, with the free exit at the discharge tank at 24.4 meters elevation and the free surface at the source tank at 21.3 meters elevation.

To find the flow rate in the pipeline, we can apply the principle of continuity. According to this principle, the flow rate in a pipe remains constant. Therefore, we can equate the flow rates at the suction side and discharge side.

Considering the diameters at both ends of the pipeline, we can calculate the respective cross-sectional areas at the suction and discharge sides. 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.

By equating the cross-sectional areas and solving for the velocity at the discharge side, we can determine the flow rate in the pipeline. This calculation involves cancelling out π, simplifying the equation, and obtaining the final answer for the flow rate.