Velocity Potential Function
Function of Velocity Potential
It is defined as a scalar function of space and time such that its negative derivative along any direction gives the component of velocity along that direction.
Remember:
- Negative sign implies flow always occurs in the direction of decreasing potential.
- Velocity potential function exists only for irrotational flow and potential flow.
- If velocity potential function satisfies the Laplace equation, then it also satisfies continuity equation and hence the flow is possible.
Flow Through Pipes
Friction Loss/Darcy Weisbach Equation
Darcy Weisbach equation.
Laminar Flow Through Circular Pipe (Hagen-Poiseuille Flow)
Shear stress (τ) distribution
The negative sign on x ∂p/∂x indicates decrease in pressure in the direction of flow. The pressure must decrease because pressure force is the only means available to compensate for resistance to the flow, the potential and kinetic energy remain constant.
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