Question

Water is flowing through a pipe that slowly gets smaller as it rises to the bathroom on your second floor (10 m high). The pipe coming into your house is 3 cm in diameter, the pressure there is 3x105 Pa, and the water is moving at .8 m/s. The diameter of the pipe in the upstairs bathroom is 1.5 cm. How fast is the water moving right before it leaves the pipe in the bathroom?

Answer 1

velocity at the out let is equal to 3.18 m/s

Step-by-step explanation:

height of the second floor = 10 m

pipe diameter(d₁) = 3 cm = 0.03 m

pressure (P₁) = 3 x 10⁵ Pa

diameter at the upstairs (d₂) = 1.5 cm = 0.015 m

A₁ =
`(\pi)/(4)d^2`

A₁ =
`(\pi)/(4)0.03^2`

A₁ = 7 × 10⁻⁴ m²

A₂ =
`(\pi)/(4)d^2`

A₂ =
`(\pi)/(4)0.015^2`

A₂ = 1.76× 10⁻⁴ m²

using continuity equation

A₁ v₁ = A₂ v₂

7 × 10⁻⁴ × 0.8 = 1.76× 10⁻⁴ × v₂

v₂ = 3.18 m/s

hence velocity at the out let is equal to 3.18 m/s