Question

A Venturi tube in 6in. in diameter at the entrance, where the pressure is 10lb/in² (gage). The throat is 4in. in diameter; there the pressure is 6lb/in² (gage). What is the flow of water?

Answer 1

The flow rate of water through the Venturi tube is 0.

Step-by-step explanation:

In order to find the flow of water through the Venturi tube, we can use Bernoulli’s equation which states that the sum of the pressure energy, kinetic energy, and potential energy per unit volume is constant.

Since the water is incompressible and there is no change in elevation, we can neglect the potential energy term. So we have:

1. At the entrance (diameter = 6in): P₁ = 10lb/in² (gage), V₁ = ?
2. At the throat (diameter = 4in): P₂ = 6lb/in² (gage), V₂ = ?

The flow rate of water can be calculated using the equation:

Q = A₁V₁ = A₂V₂

Where A₁ and A₂ are the areas of the entrance and throat respectively, and V₁ and V₂ are the velocities at the entrance and throat.

Now, let's calculate the flow rate:

A₁ = (π/4)(6in)² = 9πin²

A₂ = (π/4)(4in)² = 4πin²

Q = A₁V₁ = A₂V₂

V₁ = (Q/A₁)

V₂ = (Q/A₂)

Now substitute the known values of A₁, A₂, P₁, P₂, V₁, and V₂ into the equation and solve for Q:

[ (Q/A₁) ] = [ (Q/A₂) ]

(Q/A₁) = (Q/A₂)

(Q/9πin²) = (Q/4πin²)

(Q/9) = (Q/4)

4Q = 9Q

9Q - 4Q = 0

5Q = 0

Q = 0

Thus, the flow rate of water through the Venturi tube is 0.