Question

What is the equation of the curve AB?

I have been asked this question during a job interview.

I want to ask this question from Specific Energy topic in section Flow in Open Channels of Fluid Mechanics

Answer 1

The equation of the curve AB you're referring to is likely related to the specific energy curve in open channel flow, which is a fundamental concept in fluid mechanics. The specific energy curve represents the relationship between the flow depth and the total energy at a given location in the channel.

In the context of flow in open channels, the specific energy (E) is the sum of the flow depth (h) and the velocity head. The specific energy equation is given by:

E=h+v22gE = h + \frac{v^2}{2g}E=h+2gv2​

Where:

• $E$ = specific energy (m),
• $h$ = flow depth (m),
• $v$ = flow velocity (m/s),
• $g$ = acceleration due to gravity (9.81 m/s²).

For an open channel:

• The total energy (specific energy) is a function of both the flow depth and velocity.
• The specific energy curve, also known as the specific energy vs. flow depth curve, shows how the total energy changes with variations in the depth of flow for a given discharge.

To find the equation of the curve AB:

If you are dealing with a steady, uniform flow in an open channel, the flow rate $Q$ is related to the flow depth and velocity. For a rectangular channel, the relationship between discharge, velocity, and depth is:

$$Q=v\cdot A=v\cdot b\cdot h$$

Where:

• $b$ = width of the channel,
• $A$ = cross-sectional area of flow (for a rectangular channel, $A=b\cdot h$),
• $Q$ = discharge (m³/s).

Using the above equation, you can express the velocity $v$ in terms of the flow depth $h$ and substitute it into the specific energy equation:

E=h+(Q/(b⋅h))22gE = h + \frac{(Q / (b \cdot h))^2}{2g}E=h+2g(Q/(b⋅h))2​

This would give you a relation between specific energy (E) and flow depth (h) for a given discharge.

Curve AB:

The curve AB typically refers to the specific energy curve between two points, A and B, which could represent different flow conditions (such as subcritical and supercritical flow). This curve is essential for understanding the behavior of open channel flows and determining the flow regime (subcritical, critical, or supercritical).