Question

A water is flowing through a circular varying diameter pipe. The water completely fills the pipe at all its sections.

1- What is the water velocity of the water at the first section if you know that the diameter of the pipe at this section= 22 cm and the water is flowing at a rate of 2.5 m3/s?

2- What is the diameter of the pipe at the second section if you know that the water velocity at this section = 5.2 m/s?

Answer 1

From the continuity  equation of any volumetric flow of fluid (represented as m³ /s ) the relation of its velocity and cross sectional area through which fluid continue to flow is given as:

A₁V₁ = A₂V₂

where subscript A and V are cross sectional area and velocity respectively.

so,

1) here volumetric flow through pipe = 2.5 m³ /s and diameter of the pipe = 22 cm = 0.22 m

therefore, volumetric flow = Area x velocity

2.5 = /4 *d² x Velocity

2.5 =  /4 * 0.22² x Velocity

so, Velocity = 2.5 / ( /4 * 0.22²)

= 65.76 m/s (answer)

-----------------------------------------------------

2) similarly, with the same volumetric flow, the diameter of the second section will be = ?

Volumetric flow = Area x velocity

2.5 =  (/4 x d² ) x velocity

2.5 =   (/4 x d² ) x 5.2

d² = 2.5 / (5.2 * /4 )

= 0.612

or d = 0.612

= 0.782 m (answer)