Question

At one point in a pipeline the water's speed is 3.00 m/s and the gauge pressure is 5.00××1044 Pa.

Find the gauge pressure at a second point in the line, 11.0 m lower than the first, if the pipe diameter at the second point is twice that at the first.

Express your answer in kilopascals.

Answer 1

Given,

At point 1

Water's Speed ( ) = 3.00 m/s

Gauge Pressure ( ) =

Height of the point 1 from ground =

  Height of the point 2 from ground =

The diffrence between the two points ( ) = = 11.0 m

Density of water ( ) =

Acceleration due to gravity ( g ) = 9.8

The diameter at the second point ( ) is twice than at the first ( ).

Let the water's speed and gauge pressure at point 2 are and respectively.

For :

Applying continuity equation at both the points,

  

For :

Applying Bernoulli's theorem at both the points,

putting the given values,