In the form p1A1v1 = p2A2v2, which fundamental equation is being described?

In the form p1A1v1 = p2A2v2, which fundamental equation is being described?

• A. Continuity Equation
• B. Bernoulli Equation
• C. Energy Equation
• D. Momentum Equation

Answer: (A)

Conservation of mass in steady, one‑dimensional flow is the idea here. The mass flow rate through a section is ṁ = ρ A v. To prevent accumulation of mass, this rate must be the same at any cross-section along the flow, so ρ1 A1 v1 = ρ2 A2 v2. If the fluid is incompressible and density stays constant, this reduces to A1 v1 = A2 v2. The form shown, with a density-like term times area times velocity equal at two sections, embodies that same continuity principle. The other fundamental equations describe different relationships: Bernoulli ties together pressure and velocity along a streamline under energy conservation, the energy equation accounts for energy balance including enthalpy and temperature effects, and the momentum equation concerns forces on a control volume. Thus, this expression fundamentally expresses the continuity (mass conservation) idea.

Conservation of mass in steady, one‑dimensional flow is the idea here. The mass flow rate through a section is ṁ = ρ A v. To prevent accumulation of mass, this rate must be the same at any cross-section along the flow, so ρ1 A1 v1 = ρ2 A2 v2. If the fluid is incompressible and density stays constant, this reduces to A1 v1 = A2 v2. The form shown, with a density-like term times area times velocity equal at two sections, embodies that same continuity principle. The other fundamental equations describe different relationships: Bernoulli ties together pressure and velocity along a streamline under energy conservation, the energy equation accounts for energy balance including enthalpy and temperature effects, and the momentum equation concerns forces on a control volume. Thus, this expression fundamentally expresses the continuity (mass conservation) idea.