Question

Physics

How can we calculate the drag force and dissipation rate for pressure-driven planar flow in terms of the average velocity?

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Best Answer

To calculate the drag force and dissipation rate for pressure-driven planar flow, we can follow these steps:

- Consider the pressure-driven planar flow, which occurs between two parallel plates and is driven by a pressure gradient.
- Use the simplified Navier-Stokes equation for steady, incompressible, and laminar flow to describe the flow.
- Integrate the velocity profile over the channel height and divide by the channel height to find the average velocity.
- Calculate the drag force by multiplying the wall shear stress (obtained from the velocity gradient at the wall) by the plate area.
- Determine the dissipation rate by integrating the square of the velocity gradient over the channel height.
- Express the drag force and dissipation rate as functions of the average velocity, pressure gradient, channel height, and fluid properties.
- By following these steps, we can obtain the expressions for drag force and dissipation rate in terms of the average velocity.