Question

A fluid traveling through a horizontal pipe with a decreasing cross-sectional area experiences what kind of pressure change, assuming inviscid flow?

• A. Pressure increases
• B. Pressure decreases
• C. Pressure remains constant
• D. Pressure becomes negative

Hint:

Bernoulli Principle (Flow in Pipes). For inviscid, incompressible, steady, horizontal flow: Where velocity increases (e.g., due to decreased area via continuity), pressure decreases.

Answer 1

The Correct Option is B

Assuming steady, incompressible, inviscid flow in a horizontal pipe, we can apply Bernoulli's equation between two points along the pipe: $$ P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2 $$ (The \(\rho g h\) term is constant for a horizontal pipe and cancels out).
We also use the continuity equation for incompressible flow: \(A_1 v_1 = A_2 v_2\).
If the cross-sectional area decreases (\(A_2<A_1\)), the continuity equation implies that the velocity must increase (\(v_2>v_1\)).
According to Bernoulli's equation, if the velocity \(v\) increases, the term \(\frac{1}{2}\rho v^2\) (dynamic pressure) increases.
To keep the sum constant, the static pressure \(P\) must decrease.
Therefore, as the area decreases, velocity increases, and pressure decreases.