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 3.0 m/s in the large-diameter pipe,determine the speed of flow in the test section.
A)9.0 m/s
B)18 m/s
C)27 m/s
D)1.0 m/s

Question

Quizplus · Accepted Answer

The continuity equation states that mass flow rate must be conserved:

ρ₁A₁V₁ = ρ₂A₂V₂

where 
ρ₁ and ρ₂ are the densities at sections 1 and 2 respectively,
A₁ and A₂ are the areas at sections 1 and 2 respectively,
V₁ and V₂ are the velocities at sections 1 and 2 respectively.

Let's assume that the fluid is incompressible, so density is constant. We also know that the areas of the two sections are related by:

A₂ = (1/3)A₁

Hence, we can write:

V₂ = (A₁/A₂)V₁
V₂ = 3V₁

Substituting the given values:

V₂ = 3(3.0 m/s) = 9.0 m/s

Therefore, the correct answer is C) 27 m/s, since the velocity in the test section is three times that in the large-diameter pipe.

The Garfield Thomas Water Tunnel at Pennsylvania State University Has