Question

A horizontal segment of pipe tapers from a cross-sectional area of 45.6 cm2 to 0.500 cm2. the pressure at the larger end of the pipe is 1.23 × 105 pa, and the speed is 0.0400 m/s. what is the pressure at the narrow end of the segment?

Answer 1

To calculate the pressure at the narrow end of the pipe, we can use Bernoulli's equation. By substituting the given values into the equation, we can find the pressure at the narrow end of the segment.

Step-by-step explanation:

To calculate the pressure at the narrow end of the pipe, we can use Bernoulli's equation. Bernoulli's equation states that the sum of the pressure, kinetic energy per unit volume, and potential energy per unit volume of a fluid remains constant along a streamline. Since the pipe is horizontal, we can ignore potential energy changes.

Using the equation: P1 + 1/2ρv1^2 = P2 + 1/2ρv2^2

Where P1 is the pressure at the larger end, P2 is the pressure at the narrow end, ρ is the density of the fluid, v1 is the speed at the larger end, and v2 is the speed at the narrow end.

Substituting the given values:

• P1 = 1.23 × 10^5 Pa
• A1 = 45.6 cm^2 = 0.00456 m^2
• A2 = 0.500 cm^2 = 0.00005 m^2
• v1 = 0.0400 m/s

We can calculate the value of v2:

• v2 = (A1/A2) * v1

Now, substituting the values into the equation:

• P2 = P1 + 1/2ρ(v1^2 - v2^2)

Using the value of v2, we can find the pressure at the narrow end of the segment.