How Does Pipe Tapering Affect Pressure and Flow Rate in Fluid Dynamics?

[partech]

1. Water is flowing in a pipe from a tank to a nozzle. At some point (A) the pipe tapers from 160 mm diameter to 80 mm at point B over a certain length. Point A is 3 m above point B. The pressure at A is 100kPa and at B is 20kPa, both measured above the atmospheric pressure. The flow rate is 4m3min-1, and is in the direction from A to B.

Find the loss of pressure between A and B and express it as (i) head of water, (ii) gauge pressure and (iii) absolute pressure.




2. using the following equations:
Q=Au
to calculate the velocity at points A and B
Bernoulli’s equation





3. i first calculated the velocity at point A and B. Usings these in Bernoulli's equation to find head lost. Value = 2.26m
This is where i not sure gauge pressure would it be simply one take away the other. The take into account atmospheric pressure for the absolute pressure?

Many thanks for any help just to point me in the right direction.

 

[partech]

Here is some more information to show i have attempted the question. Please see attachments for calculations.
• Da=160mm Aa=0.0201m2
• Db=80mm Ab=5.0265x10-3m2
• Za = 3m
• Zb = 0m (Lowest Point Datum)
• Pa=100kPa
• Pb=20kPa
• Q = 4m3min-1 = 1/15 m3s-1
• Direction A to B

If you could please view and advise me on if this is correct or where i have gone wrong it would be most greatful. I am still not sure about the atmospheric and gauge pressure would this be the same pressure loss?

Many Thanks