Question

Water is travelling at 2.3 m/s through a pipe 3.2 cm in diameter. When the pipe narrows to 2.9 cm in diameter, what is the new speed, in m/s?

Answer 1

New speed of water is 2.8 m/s.

Step-by-step explanation:

It is given that,

Speed of water, v₁ = 2.3 m/s

Diameter of pipe, d₁ = 3.2 cm

Radius of pipe, r₁ = 1.6 cm = 0.016 m

Area of pipe,
`A_1=\pi(0.016)^2=0.000804\ m^2`

If the pipe narrows its diameter, d₂ = 2.9 cm

Radius, r₂ = 0.0145 m

Area of pipe,
`A_2=\pi(0.0145)^2=0.00066\ m^2`

We need to find the new speed of the water. It can be calculated using equation of continuity as :

`v_1A_1=v_2A_2`

`v_2=(v_1A_1)/(A_2)`

`v_2=(2.3\ m* 0.000804\ m^2)/(0.00066\ m^2)`

`v_2=2.8\ m/s`

So, the new speed of the water is 2.8 m/s. Hence, this is the required solution.