User:Dolphin51/Sandbox3

EngineerSteve, You believe that The fluid increase in speed entering the narrow section of a Venturi tube is caused by the decreasing Pressure Gradient between the fat and narrow sections. I disagree.

Let's look at a practical problem requiring use of Bernoulli's equation. We can compare my answer and your answer, and see where I went wrong.

Here is Bernoulli's equation for a horizontal flow expressed in units of energy per unit volume so it is applicable to liquids:

${\displaystyle P_{1}+{\frac {1}{2}}\rho (V_{1})^{2}=P_{2}+{\frac {1}{2}}\rho (V_{2})^{2}}$

Q. Here is the question. Water is flowing at the rate of 12 cubic feet per second in a pipe with a circular cross-section and area of 1 square feet. The liquid pressure in this part of the pipe is 3000 pounds per square foot. The pipe then narrows to a circular cross-section of 0.95 square feet. Use Bernoulli's equation to estimate the pressure in the narrow section.

A. Here is my answer.

1. A flow rate of 12 cu ft/s through an area of 1 sq ft gives a mean speed V₁ of 12 ft/s and V² is 144.
2. The principle of continuity shows that the mean speed of the flow V₂ in the narrow section must be ${\displaystyle {\frac {12}{0.95}}=12.63}$ ft/s and V² is 159.
3. Pressure in the first section of pipe P₁ is 3000 lb per square foot.
4. Applying Bernoulli's equation:

${\displaystyle 3000+{\frac {\rho }{2}}144=P_{2}+{\frac {\rho }{2}}159}$

${\displaystyle P_{2}=3000+{\tfrac {\rho }{2}}(144-159)}$

${\displaystyle P_{2}=3000-{\tfrac {62.4}{2}}(15)}$

${\displaystyle P_{2}=3000-468=2532}$ pounds per square foot

Feel free to post your calculations here. We can then examine the two sets of calculations and see if we get different answers; and why.

My view is that it is incorrect to say "the speed increase is caused by the decrease in pressure." I would argue that both the speed increase and the pressure decrease are caused by the change in the geometry of the pipe - the reduction in cross-section area of the pipe. You will disagree with me so I'm very interested to see your calculations to see what effect our different views have on the calculations, and the answers. If we both get the same answer it will suggest that whether we believe change in pressure causes change in speed, or vice versa, is irrelevant in the application of Bernoulli's equation. Dolphin (t) 14:38, 17 May 2025 (UTC)