In Fluid Mechanics what is the difference between yc and hc?

• Beembo
In summary: It sounds like this is just a classic case of someone who learned a regurgitated equation without learning what it actually means or where it comes from, so you may be onto something.
Beembo
When solving for the hydrostatic force on a surface we use the height to the centroid(hc), then when using the point of application we use the y coordinate of the centroid(yc), however shouldn't they be the same since they both start from the top surface and reach down to the object surface on the same axis?

It depends on how you've defined your axes. If your y-axis is taken to be downward normal to the liquid surface, then they are the same. If your y-axis is angled to make the math more convenient then ##y## and ##h## will be different (but related through ##\theta##).

Beembo said:
When solving for the hydrostatic force on a surface we use the height to the centroid(hc), then when using the point of application we use the y coordinate of the centroid(yc), however shouldn't they be the same since they both start from the top surface and reach down to the object surface on the same axis?
Hi Beembo,
A problem well described is half the battle.

While I would tend to think that you are asking about the location of the resultant force on a submerged surface, that does not come quite clear in your post.
Some questions come to mind about the axis orientation, surface shape, surface orientation for example.

256bits said:
Hi Beembo,
A problem well described is half the battle.

While I would tend to think that you are asking about the location of the resultant force on a submerged surface, that does not come quite clear in your post.
Some questions come to mind about the axis orientation, surface shape, surface orientation for example.

That was reasonably clear to me, though it involved a few assumptions, such as that the surface is planar.

That was reasonably clear to me, though it involved a few assumptions, such as that the surface is planar.
Right. The basic submerged plate problem.
Two different centroids are involved to find the location and magnitude of the resultant.
He, himself, thinking about how to describe a problem clearly could give the OP a better insight as to why that is so.

256bits said:
Right. The basic submerged plate problem.
Two different centroids are involved to find the location and magnitude of the resultant.
He, himself, thinking about how to describe a problem clearly could give the OP a better insight as to why that is so.

It sounds like this is just a classic case of someone who learned a regurgitated equation without learning what it actually means or where it comes from, so you may be onto something.

1. What is the definition of yc in fluid mechanics?

yc, also known as the critical depth, is the depth at which the specific energy of a fluid flow is at its minimum. It is a critical parameter in open channel flow calculations.

2. How is yc calculated in fluid mechanics?

The yc value can be calculated using the Manning's equation, which takes into account the slope of the channel, the roughness of the channel walls, and the discharge of the flow.

3. What is the significance of yc in fluid mechanics?

yc is important in fluid mechanics because it determines the flow regime of a channel. If the flow depth is greater than yc, the flow is considered supercritical, and if the flow depth is smaller than yc, the flow is considered subcritical.

4. What is the difference between yc and hc in fluid mechanics?

While yc refers to the critical depth of a flow, hc refers to the critical depth of a hydraulic jump. A hydraulic jump occurs when a supercritical flow encounters a sudden decrease in slope, resulting in a rapid rise in depth. The hc value is typically larger than the yc value.

5. How does yc affect the stability of a channel in fluid mechanics?

The yc value is a critical parameter in determining the stability of a channel. If the flow depth exceeds yc, the channel is considered unstable and erosion of the channel bed may occur. Therefore, it is important to properly calculate yc to ensure the stability of a channel.

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