A plastic float travels 10 feet in 4.2 seconds in a wastewater channel that is 2.4 feet wide and 1.8 feet deep. What is the flow rate in cubic feet per second?

A plastic float travels 10 feet in 4.2 seconds in a wastewater channel that is 2.4 feet wide and 1.8 feet deep. What is the flow rate in cubic feet per second?

• A. 9.8 ft3/sec
• B. 10.3 ft3/sec
• C. 11.0 ft3/sec
• D. 12.0 ft3/sec

Answer: (B)

Discharge is the amount of water flowing per second, so use Q = A × v, where A is the cross-sectional area of the channel and v is the water velocity. The float’s speed approximates the water’s mean velocity. Velocity: v = distance / time = 10 ft / 4.2 s ≈ 2.381 ft/s. Cross-sectional area: A = width × depth = 2.4 ft × 1.8 ft = 4.32 ft². Flow rate: Q = A × v ≈ 4.32 ft² × 2.381 ft/s ≈ 10.29 ft³/s, which rounds to 10.3 ft³/s. So the flow rate is about 10.3 cubic feet per second.

Discharge is the amount of water flowing per second, so use Q = A × v, where A is the cross-sectional area of the channel and v is the water velocity. The float’s speed approximates the water’s mean velocity.

Velocity: v = distance / time = 10 ft / 4.2 s ≈ 2.381 ft/s.

Cross-sectional area: A = width × depth = 2.4 ft × 1.8 ft = 4.32 ft².

Flow rate: Q = A × v ≈ 4.32 ft² × 2.381 ft/s ≈ 10.29 ft³/s, which rounds to 10.3 ft³/s.

So the flow rate is about 10.3 cubic feet per second.