At one point in a pipeline, the water's speed is 3.57 m/s and the gauge pressure is 68.7 kPa. Find the gauge pressure at a second point in the line, 18.5 m lower than the first, if the pipe diameter at the second point is twice that at the first. Remember that the density of water is 1000 kg/m3. Please give your answer in units of kPa.

The  pressure at point 2 is

Explanation:

From the question we are told that

   The speed at point 1  is  

   The  gauge pressure at point 1  is  

    The density of water is  

Let the  height at point 1 be   then the height at point two will be

Let the  diameter at point 1 be   then the diameter at point two will be

Now the continuity equation is mathematically represented as  

Here  are the area at point 1 and 2

    Now given that the are is directly proportional to the square of the diameter [i.e ]

   which can represent as

=>        

where c is a constant

  so      

=>          

=>        

Now from the continuity equation

=>    

=>    

Generally the Bernoulli equation is mathematically represented as

So  

=>    

substituting values

well clustered together.

points close on a scatter diagram