Carmen-Kozney equation has been derived using which of the following e...
Explanation: Carmen-Kozney equation has been derived using Darcy Weisbach equation which is given by h = f*l*v2/(g*D) Where h is the head loss, D is the diameter of pipe, v is the velocity of the particle and f is the dimensionless friction factor.
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Carmen-Kozney equation has been derived using which of the following e...
Derivation of Carmen-Kozney Equation:
The Carmen-Kozney equation has been derived using the Darcy-Weisbach equation. The Darcy-Weisbach equation is used to calculate the pressure loss in a pipe due to fluid flow.
Darcy-Weisbach Equation:
The Darcy-Weisbach equation relates the pressure loss in a pipe to the flow rate, pipe diameter, pipe length, and fluid properties. It is given by:
\[
\Delta P = f \frac{L}{D} \frac{\rho V^2}{2}
\]
where:
- \(\Delta P\) is the pressure loss
- \(f\) is the Darcy friction factor
- \(L\) is the pipe length
- \(D\) is the pipe diameter
- \(\rho\) is the fluid density
- \(V\) is the fluid velocity
Carmen-Kozney Equation:
The Carmen-Kozney equation is an empirical correlation used to calculate the permeability of porous media. It is derived by relating the permeability to the specific surface area of the porous medium and the porosity. The equation is given by:
\[
k = \frac{\alpha^2}{\tau^2} \frac{(1 - \varepsilon)^3}{\varepsilon^2}
\]
where:
- \(k\) is the permeability
- \(\alpha\) is the specific surface area
- \(\tau\) is the tortuosity
- \(\varepsilon\) is the porosity
The Carmen-Kozney equation is widely used in the field of porous media flow and has applications in various industries including petroleum engineering, groundwater hydrology, and soil mechanics.
Therefore, the Carmen-Kozney equation has been derived using the Darcy-Weisbach equation, which forms the basis for understanding fluid flow in porous media.