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