Consult multiple-concept example 15 to review the concepts on which this problem depends. water flowing out of a horizontal pipe emerges through a nozzle. the radius of the pipe is 1.8 cm, and the radius of the nozzle is 0.49 cm. the speed of the water in the pipe is 0.56 m/s. treat the water as an ideal fluid, and determine the absolute pressure of the water in the pipe. (the atmosphere pressure is p = 1.01 105 pa, and the density of water is rho = 1.00 103 kg/m3.)

The pressure of the water in the pipe is 129554 Pa.

Explanation:

There are wrongly written values on the proposal, the atmospheric pressure must be 101105 Pa, and the density of water 1001.03 kg/m3, those values are the ones that make sense with the known ones.

We start usign the continuity equation, and always considering point 1 a point inside the pipe and point 2 a point in the nozzle:

We want , and take into account that the areas are circular:

Substituting values we have (we don't need to convert the cm because they cancel out between them anyway):

For determining the absolute pressure of the water in the pipe we use the Bernoulli equation:

Since the tube is horizontal and those terms cancel out, so the pressure of the water in the pipe will be:

And substituting for the values we have, considering the pressure in the nozzle is the atmosphere pressure since it is exposed to it we obtain: