The Garfield Thomas water tunnel at Pennsylvania State University has a circular cross-section that constricts from a diameter of 3.6 m to the test section,which is 1.2 m in diameter.If the speed of flow is 3.5 m/s in the large-diameter pipe,determine the speed of flow in the test section.
A) 0.4 m/s
B) 3.5 m/s
C) 32 m/s
D) 4 m/s
E) 34 m/s

Question

The Garfield Thomas water tunnel at Pennsylvania State University has a circular cross-section that constricts from a diameter of 3.6 m to the test section,which is 1.2 m in diameter.If the speed of flow is 3.5 m/s in the large-diameter pipe,determine the speed of flow in the test section.
A) 0.4 m/s
B) 3.5 m/s
C) 32 m/s
D) 4 m/s
E) ​34 m/s

Quizplus · Accepted Answer

The correct answer is C.The speed of flow in the test section can be determined using the principle of continuity, which states that the mass flow rate is constant throughout a pipe. The mass flow rate is given by:```Q = Av```where:* Q is the mass flow rate (kg/s)* A is the cross-sectional area of the pipe (m^2)* v is the speed of flow (m/s)Since the mass flow rate is constant, we can write:```Q1 = Q2```where:* Q1 is the mass flow rate in the large-diameter pipe (kg/s)* Q2 is the mass flow rate in the test section (kg/s)The cross-sectional area of the large-diameter pipe is:```A1 = π(d1/2)^2 = π(3.6 m/2)^2 = 10.18 m^2```The cross-sectional area of the test section is:```A2 = π(d2/2)^2 = π(1.2 m/2)^2 = 1.13 m^2```Substituting these values into the equation for mass flow rate, we get:```A1v1 = A2v2```Solving for v2, we get:```v2 = (A1v1)/A2 = (10.18 m^2 * 3.5 m/s)/1.13 m^2 = 32 m/s```Therefore, the speed of flow in the test section is 32 m/s.

The Garfield Thomas Water Tunnel at Pennsylvania State University Has