At one point in a pipeline, the water's speed is 3.00 and the gauge pressure is 4.00×104 . Find the gauge pressure at a second point in the line 11.0 lower than the first if the pipe diameter at the second point is twice that at the first.

Question

I've been trying to use Bernoulli's equasion to find the gauge pressure, but it's not working for me.

Answer 1

You need to provide units (dimensions) for pressure and speed and height or we can't help you. Numbers are not enough. 1 mile is not 1 inch.

You are correct in using the Bernoulli equation. You also need to use the continuity equation: V * Area = constant.

When the pipe diameter gets twice as large, the velocity becomes 1/4 of the previous value.

P + (1/2) (rho) V^2 + (rho) g H = constant

(rho is the density of water, in the appropriate units)

The change in H (height) and V will tell you the change in gauge pressure. It will be higher where the velocity is less and the elevation lower.

Answer 2

Sorry about the lack of units...but your input helped me to solve it. I wasn't figuring the velocity correctly for the lower portion of the tube! Thanks so much!!