Question

A water tunnel has a circular cross-section with a radius of 1.8 m in its main section. In a test section of the tunnel the radius constricts to a value of 0.60 m. If the speed of water flow is 3.0 m/s in the main section, determine the speed of water flow in the test section.

Answer 1

To solve this problem it is necessary to apply the concepts related to the concepts to continuity.

From the continuity equation we know that

`A_1V_1 = A_2 V_2`

Where,

A = Cross-sectional Area

V = Velocity

In a circle the area is given by

`A_1 = \pi r_1^2\\A_2 = \pi r_2^2`

Therefore replacing with our values we have that

`A_1 = \pi r_1^2\\A_1 = \pi 1.8^2\\A_1 = 10.278m^2`

While the area two is defined as

`A_2 = \pi r_2^2\\A_2 = \pi 0.6^2\\A_2 = 1.13m^2`

Applying the continuity equation we have to

`A_1V_1 = A_2 V_2`

`(10.278)(3)= (1.13) V_2`

`V_2 = 27.28m/s`

Therefore the speed of water flow in the test section is 27.28m/s