Question

1. a weir is a dam that is built across a river to regulate the flow of water. the flow rate, \\(q\\) (in cubic feet per second), can be calculated using the formula \\(q = 3.367lh^{3/2}\\), where \\(l\\) is the length (in feet) of the bottom of the spillway and \\(h\\) is the depth (in feet) of the water on the spillway. determine the flow rate of a weir with a spillway that is 20 feet long and has a water depth of 5 feet. round your answer to the nearest cubic foot per second.

Explanation:

⚡ Using what you learned: Integer and Rational Exponents

Step 1: Identify given values

Identify the variables from the problem statement:

• Formula: \( Q = 3.367 \cdot l \cdot h^{3/2} \)
• Length \( l = 20 \)
• Depth \( h = 5 \)

Step 2: Substitute and calculate

Substitute the values into the formula:

$$ Q = 3.367 \cdot 20 \cdot 5^{3/2} $$

Calculate \( 5^{3/2} \):

$$ 5^{3/2} = 5 \sqrt{5} \approx 11.1803 $$

Calculate \( Q \):

$$ Q = 3.367 \cdot 20 \cdot 11.1803 \approx 752.88 $$

Step 3: Round to the nearest integer

Round \( 752.88 \) to the nearest cubic foot per second:

$$ Q \approx 753 $$

Answer:

753 cubic feet per second