Question

Air flows steadily between two cross sections in a long straight section of 0.25m inside diameter pipe. The static temperature and pressure at each section is indicated in the figure. If the average air velocity at section 2 is 320 m/s, determine the average air velocity at section 1.

Answer 1

The average air velocity at section 1 of the pipe is 320 m/s. This is calculated using the equation Q = Av, where A is the cross-sectional area and v is the average velocity. The cross-sectional areas at section 1 and section 2 are the same, so we can set up an equation and solve for v1.

Step-by-step explanation:

The flow rate of a fluid through a pipe can be determined using the equation Q = Av, where A is the cross-sectional area and v is the average velocity. In this case, we are given the average air velocity at section 2 (v2) and need to find the average air velocity at section 1 (v1).

Since the pipe is a long straight section with a constant diameter, we can assume that the cross-sectional areas at section 1 and section 2 are the same. Therefore, we can set up the following equation:

(A1)(v1) = (A2)(v2)

Substituting the given values, we can solve for v1:

v1 = (A2)(v2) / A1

Given that the pipe has a diameter of 0.25m, we can calculate the cross-sectional areas A1 and A2 using the formula for the area of a circle:

A = π(r^2)

Using the diameter, we find that the radius is 0.125m. Plugging the values into the formula, we get:

A1 = A2 = π(0.125^2) = 0.0491m^2

Substituting these values into the equation, we get:

v1 = (0.0491)(320) / 0.0491 = 320 m/s

Therefore, the average air velocity at section 1 is 320 m/s.