Question

To water the yard, you use a hose with a diameter of 2.5 cm. Water flows from the hose with a speed of 1.1 m/s. If you partially block the end of the hose so the effective diameter is now 0.55 cm, with what speed does water spray from the hose? Answer in m/s

Answer 1

The diameter of hose at first end, d1 = 2.5 cm = 0.025 m

So the area of hose at first end, A1 = π(d1/2)^2 = 4.9 * 10^-4 m^2

The speed at first end, V1 = 1.1 m/s

The deameter of hose at second end, d2 = 0.55 cm = 0.0055 m

So the area of hose at second end, A2 = π(d2/2)^2 = 2.37 * 10^-5 m^2

Let the speed at the second end of the hose = V2

We have an equation from the equation of continuity as

           A2V2 = A1V1

From the above we have

           V2 = A1V1 / A2 = 22.74 m/s

So the speed of water spray at the second end of the hose is 22.74 m/s