Question

Gas flows through the pipe of FIGURE Q14.10. You can’t see into the pipe to know how the inner diameter changes. Rank in order, from largest to smallest, the gas speeds v_a , v_b , and v_c at points a, b, and c. Explain.

Short answer

Velocities are v_b > v_a > v_c

Step-by-step solution

Given Information

Gas through pipe is given in the figure as below

Explanation

Bernoulli's theorem is implied by the conservation of mass and energy in fluid flow.

This means

$P_1+\frac{1}{2}\rho v_1^2+\rho g{h}_1=P_2+\frac{1}{2}\rho v_2^2+\rho g{h}_2=Cons\tan t$

From the given figure, from the level of liquid, we can say that

P_c > P_a > P_b

From the Bernoulli's theorem v_b > v_a > v_c.