I am trying to understand the fundamental concepts of fluid dynamics. Lets say I have

1.The larger end has a diameter of 8cm and Area 50.26cm2.

2.The small side has a diameter of 3cm and Area 7.0685cm2.

3.The water jet exerts a force of 87N at the smaller end.

  1. Water Entering the pipe is art 20degrees C

I know that :

1 - There's a change in cross-sectional area: A1 > A2

2 - Thanks to conservation of mass, (1) implies V2 > V1

3 - Thanks to Bernoulli, (2) implies p2 < p1

I am assuming a steady flow and no frictions and that the liquid is water, how can I find the velocity at the smaller end of the nozzle ?

I have calculate the Pressure using P = F/A to get a P2 of 12.3N/cm2.

However I am getting stuck in calculating P1 and V2

I have tried using Bernoulli's Equation however, I do not know P1 which is leaving me with more than one unknown.

Any Help would be appreciated.



1 Answer 1


You can use the continuity equation in the form $A_1 V_1=A_2 V_2$. However, there's not enough information given in your problem. You need at least one more quantity (a flow rate, velocity, or a pressure somewhere). The temperature of the water is spurious information.

I will note that the formulation of this problem looks very strange, not to use a harsher term: There is no "jet" in this problem, and it is entirely unclear what the phrase "the water jet exerts a force of 87N at the smaller end" could possibly mean.

Update after OP was updated with the final image:

Ahh, this is an entirely different problem now. You had left out crucial information. For this problem you need to use conservation of momentum in finite volumes to determine your flow rate. Choose a control volume that has inflow in the horizontal direction from the jet emanating from the pipe. You can use conservation of momentum in the horizontal direction to link the force you were given to the flow rate. This provides the missing information above.

  • $\begingroup$ I am sure that I have not other quantity given. Just the diameter of each end of the pipe and the force exerted by the water leaving the small end of the pipe (87N). I also have a type of manometer (Mercury Filled) connected to each end of the pipe showing that there is a greater pressure at the larger end of the pipe. $\endgroup$
    – rrz0
    Jan 14, 2017 at 14:25
  • $\begingroup$ Would I be able to find the force at the narrow end of the pipe using P = F/A ? $\endgroup$
    – rrz0
    Jan 14, 2017 at 14:27
  • $\begingroup$ If you know the difference in fluid levels in the manometers you can calculate the pressure difference. The problem cannot be solved without additional information. $\endgroup$
    – Pirx
    Jan 14, 2017 at 14:27
  • $\begingroup$ No I do not have that difference. That is another question asked later on in the same problem. $\endgroup$
    – rrz0
    Jan 14, 2017 at 14:28
  • $\begingroup$ I have uploaded the original image, excuse the missing information. I thought it was not relevant to find the answer for the first question, and that was my mistake. It is unclear to me, what you mean by Choose a control volume $\endgroup$
    – rrz0
    Jan 14, 2017 at 14:42

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