Question

A 7.7 cm diameter horizontal pipe gradually narrows to 6.0 cm . When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 34.0 kPa and 22.8 kPa , respectively. What is the volume rate of flow?

Answer 1

Given diameter of section 1 is d₁=7.7cm=0.077m. The radius is r₁=d₁/2 The area of section 1 is

Given diameter of section 2 is d₂=6.0cm=0.06m. The radius is r₂=d₂/2 The area of section 2 is

Using continuity equation, the rate of flow in both sections are equal

Applying Bernoulli's Principle in the two sections

We are given that the pipe is horizontal, z₁=z₂

Using (2)

Using (1), the flow rate is

Substituting , , , , we get