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The Huka Falls on the Waikato River is one of New Zealand's most visited natural tourist attractions. On average the river has a flow rate of about 300,000 L/s. At the gorge, the river narrows to 21 m wide and averages 21 m deep.(a) What is the average speed (in m/s) of the river in the gorge in m/s?(b) What is the average speed (in m/s) of the water in the river downstream of the falls when it widens to 64 m and its depth increases to an average of 45 m in m/s?

Sagot :

a) We would calculate the average speed by applying the formula,

v = Q/A

where

v is the average speed

Q is the flow rate

A is the cross sectional area

From the information given,

width = 21

depth = 21

A = 21 x 21 = 441 m^2

Q = 300,000 L/s

Recall, 1 L = 10^-3 m^3

Q = 300,000 x 10^-3 m^3/s

v = 300,000 x 10^-3/441

Average speed = 0.68 m/s

b) In this scenario,

width = 64

depth = 45

Area = 64 x 45 = 2880 m^2

v = 300,000 x 10^-3/2880

v = 0.104 m/s

the average speed (in m/s) of the water in the river downstream of the falls when it widens to 64 m and its depth increases to an average of 45 m is 0.104 m/s

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