Question 9.11: Niagara Falls GOAL Apply the equation of continuity. PROBLEM...

Niagara Falls

GOAL Apply the equation of continuity.

PROBLEM Each second, 5 525 m³ of water flows over the 670-m-wide cliff of the Horseshoe Falls portion of Niagara Falls. The water is approximately 2 m deep as it reaches the cliff. Estimate its speed at that instant.

STRATEGY This is an estimate, so only one significant figure will be retained in the answer. The volume flow rate is given, and, according to the equation of continuity, is a constant equal to Av. Find the cross-sectional area, substitute, and solve for the speed.

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Calculate the cross-sectional area of the water as it reaches the edge of the cliff:

A = (670 m )(2 m ) = 1340 m²

Multiply this result by the speed and set it equal to the flow rate. Then solve for v:

Av = volume flow rate

(1 340 m²)v = 5 525 m³ /s     →    v ≈ 4 m/s

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