The continuity equation states that for a constant mass flow rate, if the cross sectional area of a channel is decreased, then velocity is increased. What happens if the channel has high walls and is open to the environment, meaning that it's not an enclosed pipe? If the width of the channel begins to decrease as the wall begin to close in, will the flow retain the same height and move faster or will it retain the same velocity and have a higher height? If its both, how can I determine whether height or velocity will be greater impacted?

Thank you!


1 Answer 1


If it is a steady state flow, the pressure difference which drives the flowrate will be the same as the pressure loss due to friction and turbulence. For the open channel, you will need to use hydraulic diameter $D_H$: $$DH = \frac{4A}{P}$$ where $A$ is the flow cross-section and $P$ is the wetted perimeter.

This you can use with Darcy-Weisbach equation for pressure loss and Bernoulli equation accounting for mean flow section height differences.

Combining these 3 things together should lead to a solution to your problem.

  • $\begingroup$ So height differences will exist, meaning that height of the fluid will change with decreasing width not the velocity? $\endgroup$
    – ARJ
    Commented Aug 26, 2022 at 23:25
  • $\begingroup$ I think in general both the height and the velocity will change. But it should be also possible to find situations, where only one of these variables change. $\endgroup$ Commented Aug 27, 2022 at 7:55

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