Water flows from the pipe shown in the figure with a speed of 3.0m/s

What is the height h of the standing column of water? I wrote 5.37m, which was wrong. I have figured it out, The answer should be 4.34.

open 5.0 cm2 4.0 m 10 cm2

The water pressure when it exits into that atmosphere is zero gauge pressure (atmospheric pressure only) THat is the trick to solving this.

First find the velocity at point 1.

Q = A1 * V1 = A2 * V2

V1 = (A2/A1) V2

V1 = (5.0 cm^2 / 10 cm^2) 3.0 m/s

V1 = 1.5 m/s

NOw use burnouli's equation.

(V1/2) + (g * Z1) + (P1/rho) = (V2/2) + (g * Z2) + (P2/rho)

P2 = zero, so cancel it out and solve for P1

P1 = rho [((1/2) (V2^2 - V1^2)) + g (z2 - z1)]

And we know z2 - z1 = 4.0 m

and rho is 1000 kg/m^3

P1 = 42575 Pa = 42.575 kPa

Now just convert that to "centimeters of water column", which is also a pressure measurement.

1 cm of water = 98.1 Pa

So P1 = 42575 Pa * (1 cm water / 98.1 Pa) * (1 m/ 100 cm)

P1 = 4.34 meters of water, so

H = 4.34 meters ans.