The problem involves evaluating the flow rate $Q$ through a weir using the given formula:

$Q = \frac{2}{3} B \sqrt{2g} H^{3/2}$

Given:

• $B = 3.0 \, \text{m}$ (breadth)
• $H = 0.8 \, \text{m}$ (depth of flow)
• $g = 9.81 \, \text{m/s}^2$ (acceleration due to gravity)

Substitution and Calculation:

1. Substitute $B$, $H$, and $g$ into the formula.
2. Perform the calculation step-by-step.

Let me calculate this: Given values B = 3.0 # breadth in meters H = 0.8 # depth of flow in meters g = 9.81 # acceleration due to gravity in m/s^2

Calculate the flow rate Q

Q = (2/3) * B * ((2 * g) ** 0.5) * (H ** (3/2)) QThe flow rate through the weir is approximately $Q = 6.34 \, \text{m}^3/\text{s}$.

Would you like a detailed explanation of each step, or do you have any other questions?

Here are 5 related questions to explore further:

1. How does the flow rate change if the depth of flow $H$ is doubled?
2. What role does gravity $g$ play in determining the flow rate?
3. How would the flow rate be affected if the breadth $B$ was halved?
4. Can this equation be used for different types of weirs? Why or why not?
5. How does the $H^{3/2}$ term influence the sensitivity of flow rate to changes in depth?

Tip:

For problems involving square roots or exponents, simplifying constants like $\sqrt{2g}$ early in calculations can reduce the risk of errors and speed up repetitive computations.