Question

Air is flowing steadily through a horizontal, constant diameter pipe as shown below. The pipe wall is heated uniformly so that the temperature of the air increases as the air flows through the pipe. You may assume that the air temperature is constant across the cross-section at any length down the pipe. If the air pressure remains constant (pressure drop is small enough to ignore), what can you say about the average velocity of air in the pipe?

A. velocity will decrease because hot pipe walls will increase friction in flowing air
B. velocity will increase because increased temperature indicates the air molecules are moving faster and have higher kinetic energy
C. velocity will increase in the flow direction because density decreases as air temperature increases
D.velocity remains constant since flow is steady
E. velocity remains constant because pipe is rigid so air can't expand or change density

Answer 1

With a constant air pressure and increasing temperature in a pipe with constant diameter, the average velocity of the air increases due to the decrease in air density, as explained by the continuity equation.

Step-by-step explanation:

If the air pressure remains constant and the temperature of the air increases, according to the principles of fluid dynamics, the density of the air will decrease. This is due to the fact that warmer air expands and has fewer molecules per unit volume. From the continuity equation, which states that the mass flow rate must remain constant in a steady flow (Q = ρAv, where ρ is the density, A is the cross-sectional area, and v is the velocity), it follows that if the pipe diameter is constant and the density decreases, the velocity must increase to compensate. Therefore, it would be correct to say that the average velocity of air in the pipe would increase because the density decreases as air temperature increases (option C).