Question

To water the yard, you use a hose with a diameter of 3.0 cm. Water flows from the hose with a speed of 2.2 m/s. If you partially block the end of the hose so the effective diameter is now 0.50 cm, with what speed does water spray from the hose

Answer 1

v₂ = 79.69 m/s

Step-by-step explanation:

The initial diameter of the hose, d₁ = 3.0 cm = 0.03 m

Initial Cross Sectional Area, A₁ = πd₁²/4

A₁ = (π* 0.03²)/4

A₁ = 0.00071 m²

The initial speed of water from the hose, v₁ = 2.2 m/s

The diameter of the hose after blocking the end, d₂ = 0.50 cm = 0.005 m

Cross Sectional Area of the hose after blocking the end, A₂ = πd₂²/4

A₂ = (π* 0.005²)/4

A₂ = 0.0000196 m²

To get the speed, v₂, at which the water spray from the hose after blocking the end, we will use the continuity equation:

A₁v₁ = A₂v₂

0.00071 * 2.2 = 0.0000196 v₂

0.001562 = 0.0000196 v₂

v₂ = 0.001562/0.0000196

v₂ = 79.69 m/s