Question

Fluid is flowing horizontally at 100 gpm from a 2-in-diameter pipe to a 1-in-diameter pipe, as shown in Figure 3-41. If the pressure at point 1 is 10 psi, find the pressure at point 2. The specific gravity of the fluid is 0.9.

Answer 1

To find the pressure at point 2, we can use the principle of continuity, which states that the mass flow rate of an incompressible fluid remains constant.

Given that the flow rate is 100 gpm (gallons per minute), we need to convert it to a consistent unit. Let's convert it to cubic feet per second (cfs) for convenience.

Using the conversion factor of 1 gpm = 0.002228 cfs, we find that the flow rate is approximately 0.2228 cfs.

Now, we can use the equation for the continuity principle:

A1 * V1 = A2 * V2

where A1 and A2 are the cross-sectional areas of the pipes at points 1 and 2, respectively, and V1 and V2 are the velocities of the fluid at those points.

Given that the diameter of the 2-inch pipe is 2 inches and the diameter of the 1-inch pipe is 1 inch, we can calculate the cross-sectional areas:

A1 = π * (2/12)^2 = 0.03491 square feet
A2 = π * (1/12)^2 = 0.00873 square feet

Since the fluid is flowing horizontally, the velocity remains constant. Therefore, V1 = V2.

Now, we can rearrange the equation to solve for V2:

V2 = (A1 * V1) / A2

Substituting the values, we have:

V2 = (0.03491 * V1) / 0.00873

To find the pressure at point 2, we can use Bernoulli's equation, which relates the pressure, velocity, and height of a fluid.

P1 + (0.5 * ρ * V1^2) + (ρ * g * h1) = P2 + (0.5 * ρ * V2^2) + (ρ * g * h2)

where P1 and P2 are the pressures at points 1 and 2, respectively, ρ is the density of the fluid, V1 and V2 are the velocities at those points, g is the acceleration due to gravity, and h1 and h2 are the heights of the fluid at those points.

Given that the fluid is flowing horizontally, the heights h1 and h2 can be considered the same, so they cancel out in the equation.

Also, since the fluid is incompressible,

Answer 2

Answer: The pressure at point 2 is approximately 10.000399 psi.

Step-by-step explanation:

1. Convert the flow rate to cubic feet per second (cfs).

2. Calculate the cross-sectional area at point 1.

3. Use the continuity equation to find the velocity at point 1.

4. Calculate the density of the fluid based on its specific gravity.

5. Apply Bernoulli's equation to find the pressure at point 2.

6. The pressure at point 2 is approximately 10.000399 psi.