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