Water flows in a horizontal pipeline at a steady flow rate of 0.03 m3 s-1. The...

Water flows in a horizontal pipeline at a steady flow rate of 0.03 m3 s-1. The pipeline terminates with a reducing bend that deflects the water upwards at an angle of 45 degrees, as shown in Figure QB2. The water issues into the atmosphere. The area of the pipe is 150 x 10-4 m2 and the area at the exit to the bend is 25 x 10-4 m2. The gauge pressure at the inlet to the bend is 73.9 kN m-2. The mass of water in the bend is 50 kg.

Determine the resultant force on the bend due to the water flow

Solutions

Expert Solution

From the reynold's transport theorem calculated forces are on water

For forces calculations

First term in the right side becomes zero because control volume is not changing with time

pressure is neglected at outlet because inlet pressure is gauge pressure

substituting these values

it indicates it is in negative x-direction but on bend it will in positive x direction i.e 784.23 N

It indicates it is in positive y axis but on bend it is in negative y direction ie -424.26 N

so resultant force is

it will be in 4th quadrant

samet mamat answered 1 year ago

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