The Darcy equation expresses the relationship between the pressure head (P), viscosity (μ), flow velocity (u), and diameter (D) of a fluid flowing through a clo...
The Darcy equation expresses the relationship between the pressure head (P), viscosity (μ), flow velocity (u), and diameter (D) of a fluid flowing through a closed conduit. It helps predict the pressure drop in a pipe due to friction.
The Darcy equation is given by:
P = μ(u² - u²_s²)
where:
P is the pressure head
μ is the viscosity
u is the flow velocity
u²_s is the square of the flow velocity in the steady state
Example:
A pipe has a diameter of 0.01 m and flows water with a velocity of 0.1 m/s. If the viscosity of water is 10^(-6) m²/s, then the Darcy equation would be:
P = 10^(-6)(0.1² - 0.1²²)
P = 0.001 Pa
This means that the pressure head drops by 0.001 Pa due to friction as the fluid flows through the pipe