A constant-velocity flow enters a wide channel as shown in the figure below. At

Question

A constant-velocity flow enters a wide channel as shown in the figure below. At some distance downstream, the velocity profile is parabolic. The flow does not vary across the channel and can be considered steady. i. Is the flow in this section of the channel uniform? ii. Is the flow in this section of the channel one-, two-, or three-dimensional? iii. Is there any local acceleration in this section of the channel? iv. Is there any convective acceleration in this section of the channel? v. Sketch a suitable control volume that you could use if you wanted to find the force exerted on the channel bottom by the flow.

Explanation / Answer

i) Uniform flow relates to a condition over a certain length or reach of a stream and can occur only during steady flow condition and the depth of flow is same at every section of the channel.

So the flow is non- uniform since the flow depth varies from 0.75 ft to 1 ft.

ii) The flow is considered one-dimensional when variations of pressure and velocity occurs along the length of the channel, but any variation over the cross-section is assumed negligible.

here the flow does not vary across the channel so the flow is one dimensional.

iii) Local acceleration is defined as the rate of change of velocity with respect to time at a given point in a flow field.Here the change in velocity is with respect to change in position of fluid particles.

So there is no local acceleration in this section

iv) Convective acceleration is defined as the rate of change of velocity due to the change of position of fluid particles in a fluid flow.

So there is convective acceleration in this section of the channel.

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