In incompressible fluid flow, what quantity is conserved along a streamline?

In incompressible fluid flow, what quantity is conserved along a streamline?

• A. Pressure
• B. Volumetric flow rate
• C. Temperature
• D. Density

Answer: (B)

In incompressible flow the amount of fluid passing a given cross-section per unit time stays the same as you move along a streamline. That means the volumetric flow rate, Q = velocity times cross-sectional area, is conserved along the streamline. The density is constant in an incompressible fluid, so the mass flow rate ṁ = ρQ is also constant; the fluid simply speeds up or slows down as the cross-sectional area changes to keep the same volume per second moving through each section. Pressure can change along a streamline as the fluid accelerates or decelerates, and temperature can vary due to heating or cooling effects, so they aren’t generally conserved individually. Density remains constant by assumption, but the key conserved quantity that ties together different cross-sections along the streamline is the volumetric flow rate.

In incompressible flow the amount of fluid passing a given cross-section per unit time stays the same as you move along a streamline. That means the volumetric flow rate, Q = velocity times cross-sectional area, is conserved along the streamline. The density is constant in an incompressible fluid, so the mass flow rate ṁ = ρQ is also constant; the fluid simply speeds up or slows down as the cross-sectional area changes to keep the same volume per second moving through each section.

Pressure can change along a streamline as the fluid accelerates or decelerates, and temperature can vary due to heating or cooling effects, so they aren’t generally conserved individually. Density remains constant by assumption, but the key conserved quantity that ties together different cross-sections along the streamline is the volumetric flow rate.