Question

A garden hose with a small puncture is stretched horizontally along the ground. The hose is attached to an open water faucet at one end and a closed nozzle at the other end. As you might suspect, water pressure builds up and water squirts vertically out of the puncture to a height of 0.73 m. Determine the pressure inside the hose. (Enter your answer to the nearest 1000 Pa.)

_____________Pa

Answer 1

A garden hose with a small puncture is stretched horizontally along the ground. The hose is attached to an open water faucet at one end and a closed nozzle at the other end.

Height up to which water squirts vertically out of the puncture is, h₂ = 0.73 m

Let A be the area of cross section of the hose.

From the Bernoulli's equation we can write,

P₁ + (1/2) v₁² + gh₁ = P₂ + (1/2) v₂² + gh₂

Since the puncture is small, the velocity of water exiting this puncture will be grater than the velocity of water flowing inside the hose. Since, we neither know the cross sectional area of the hose, nor the area of the puncture in the hose and velocity of the water inside the hose, we assume that the area of cross section of the hose is equal to the area of the puncture so that the velocity of the water both inside the hose and at the puncture is the same. Since the hose is on the ground, h₁ = 0 m. Also, P₂ = 0 as water in the open experiences no pressure.

Thus, we can write

P₁ = gh₂

where gh₂ is the potential energy per unit volume.

= 1000 kg/m³and g = 9.8 m/s²

So,

P₁ = 1000 kg/m³ * 9.8 m/s² * 0.73 m

P₁ = 7154 kg/m.s² 7 kPa is the pressure inside the hose.