Answer :
The flow speed of the gas in a pipeline with a diameter of 0.250 m, given the flow rate of 1.55 m³/s, is approximately 31.57 m/s.
The question involves using the concept of flow rate in a pipe to determine the flow speed of the gas. The flow rate (volume per unit time) is given as 1.55 m³/s, and the diameter of the pipe is 0.250 m.
To calculate the flow speed, we use the formula for the flow rate, which is
Q = vA,
where Q is the flow rate, v is the flow velocity, and A is the cross-sectional area. The area A can be calculated using the formula for the area of a circle,
A = π(d/2)²,
where d is the diameter of the pipe.
First, calculate the cross-sectional area:
A = π(0.250/2)²
= π(0.125)²
≈ 0.0491 m²
Now, use the flow rate and the area to find the flow speed:
v = Q / A
= 1.55 m³/s / 0.0491 m²
≈ 31.57 m/s
Therefore, the flow speed of the gas in the pipeline is approximately 31.57 meters per second.
