Question

A garden hose is attached to a water faucet on one end and a spray nozzle on the other end. The water faucet is turned on, but the nozzle is turned off so that no water flows through the hose. The hose lies horizontally on the ground, and a stream of water sprays vertically out of a small leak to a height of 0.78 m.
What is the pressure inside the hose?

Answer 1

To solve this problem it is necessary to use the concepts related to pressure depending on the depth (or height) in which the object is on that fluid. By definition this expression is given as

$P = P_{atm} +\rho gh$

Where,

$P_{atm} =$ Atmospheric Pressure

$\rho =$Density, water at this case

g = Gravity

h = Height

The equation basically tells us that under a reference pressure, which is terrestrial, as one of the three variables (gravity, density or height) increases the pressure exerted on the body. In this case density and gravity are constant variables. The only variable that changes in the frame of reference is the height.

Our values are given as

$P_{atm} = 1.013*10^5Pa$

$\rho = 1000Kg/m^3$

$g = 9.8m/s^2$

$h = 0.78m$

Replacing at the equation we have,

$P = P_{atm} +\rho gh$

$P = 1.013*10^5 +(1000)(9.8)(0.78)$

$P = 108944Pa$

$P = 0.1089Mpa$

Therefore the pressure inside the hose is 0.1089Mpa