For incompressible, steady flow, which relation expresses the continuity equation between two cross-sections?

• A. A1 v1 + A2 v2 = constant
• B. A1 v1 = A2 v2
• C. ρ A1 v1 = ρ A2 v2
• D. v1/v2 = A2/A1

Answer: (B)

The main idea here is that in incompressible, steady flow the amount of fluid flowing through any cross-section per unit time stays the same as you move along the path. That means the volumetric flow rate, which is the product of cross-sectional area and velocity, is constant between two sections. Expressed plainly, A1 times v1 equals A2 times v2. Since the fluid is incompressible, its density stays constant, so any form that includes density ends up reducing to this same relation. The direct way to state it is A1 v1 = A2 v2, though you can also rearrange it to a ratio form like v1/v2 = A2/A1, which conveys the same idea.