Water is flowing through a V-shaped weir, which has a 30° vertex. The flow rate is 7.0 x 10⁴ kg/s and the speed of the flow is 5.0 m/s. What is the distance from the surface of the water to the vertex? A) 3.6 m B) 7.2 m C) 4.8 m D) 9.6 m E) 14.4 m

Question

Quizplus · Accepted Answer

The flow rate can be represented by the equation Q = Av, where Q is the flow rate, A is the cross-sectional area of the water, and v is the speed of the water.

In this case, we know Q = 7.0 x 10^14 kg/s and v = 5.0 m/s. To find A, we need to use the formula for the cross-sectional area of a triangular weir:

A = (2/3)H^2 tan(theta/2)

where H is the height of the water, and theta is the angle of the vertex. Plugging in the given values, we get:

7.0 x 10^14 = A(5.0) 
A = 1.4 x 10^15 m^2/s

1.4 x 10^15 = (2/3)H^2 tan(15) 
H = 7.2 meters

Therefore, the distance from the surface of the water to the vertex is 7.2 meters.

The correct choice is B.

Water Is Flowing Through a V-Shaped Weir, Which Has a 30°