Derive the formula for actuai flow through a trianguiar notch taking C to be 0.62

The flow rate (Q) through a triangular notch (also known as a V-notch weir) can be calculated using the formula:

Q = C * (8/15) * (2g)^0.5 * tan(θ/2) * H^(5/2)

Where:

• Q is the flow rate
• C is the discharge coefficient (0.62 in this case)
• g is the acceleration due to gravity
• θ is the angle of the V-notch
• H is the height of the liquid above the bottom of the notch

Here are the steps to derive this formula:

1. Start with the basic formula for flow rate over a weir: Q = C * L * H^(3/2), where L is the length of the weir. For a V-notch weir, the length of the weir is not a constant, but changes with the height of the liquid.

2. The length of the weir can be expressed in terms of the angle of the V-notch and the height of the liquid: L = 2 * H * tan(θ/2).

3. Substitute this expression for L into the basic formula for flow rate over a weir: Q = C * 2 * H * tan(θ/2) * H^(3/2) = C * 2 * tan(θ/2) * H^(5/2).

4. The factor of 2 can be combined with the discharge coefficient to give a new coefficient: Q = (2C) * tan(θ/2) * H^(5/2).

5. The formula for flow rate through a triangular notch is then: Q = C * (8/15) * (2g)^0.5 * tan(θ/2) * H^(5/2).

This formula assumes that the flow is free-flowing (i.e., the downstream water level does not affect the flow rate), and that the notch is sharp (i.e., the thickness of the notch is much less than the height of the liquid).