Question

Which equation would best describe the conservation of momentum for fluid flow in pipes?

• A. Bernoulli's equation
• B. Navier-Stokes equation
• C. Continuity equation
• D. Euler's equation

Hint:

Fundamental Fluid Equations. Continuity Eq: Mass conservation. Navier-Stokes Eq: Momentum conservation (viscous flow). Euler Eq: Momentum conservation (inviscid flow). Bernoulli Eq: Energy conservation (derived from Euler for ideal flow).

Answer 1

The Correct Option is B

- Bernoulli's equation: Represents conservation of energy along a streamline for ideal (inviscid, incompressible, steady) flow.
- Navier-Stokes equations: These are the fundamental equations of motion for viscous fluid flow.
They are derived by applying Newton's second law (conservation of momentum) to a fluid element, considering pressure, gravitational, and viscous forces.
They provide the most comprehensive description of momentum conservation for real fluid flow, including pipe flow.
- Continuity equation: Represents conservation of mass.
- Euler's equation: Represents conservation of momentum for *inviscid* (ideal) fluid flow.
Since pipe flow typically involves viscosity (friction), the Navier-Stokes equations provide the most accurate description based on momentum conservation for general fluid flow in pipes.