We have water flowing in an open channel. A small tube is placed in the channel, and the water raises to a height "l" above the water surface. The distance from the water surface to point 1/2 (points are at same height) is d. At point 1 the fluid velocity is V1 and at point 2 it is zero (stagnation point). Calculate the water velocity V1. (Figure below for help)
First I calculate the stagnation pressure Ps, by using Bernoulli from 1 to 2. This yields:
(1/2)*V1^2 + P1/rho = 0 + P2/rho
Ps = rho*(1/2)*V1^2 + P1
Then I calculate the pressure through the tube, where we have hydrostatic conditions. P0 is the atmospheric pressure.:
Ps = P0 + rhogl + rhogd.
My question is:
under which conditions can we assume that P1 = rhogd, i.e. under which conditions can we assume that the pressure at point 1 is independent of the fluid flow at that point? Is it only when the fluid flow is ONLY horizontal?