An irrigation channel has a rectangular cross section of 1.5 ft deep x 11 ft wide on the input side. On the far end of the channel, the channel expands to 6 ft wide while maintaining the same depth. If the water flowing into the channel has a speed of 30 ft/sec, calculate the velocity of the water flow on the far end of the channel.

Question

Physics

Arnav Beard

25 September, 05:08

An irrigation channel has a rectangular cross section of 1.5 ft deep x 11 ft wide on the input side. On the far end of the channel, the channel expands to 6 ft wide while maintaining the same depth. If the water flowing into the channel has a speed of 30 ft/sec, calculate the velocity of the water flow on the far end of the channel.

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Jeffery Mays · Answer 1

55 ft/s

Explanation:

A₁ = Area of rectangular cross-section at input side = 1.5 x 11 = 16.5 ft²

A₂ = Area of rectangular cross-section at far end = 1.5 x 6 = 9 ft²

v₁ = speed of water at the input side of channel = 30 ft/s

v₂ = speed of water at the input side of channel = ?

Using equation of continuity

A₁ v₁ = A₂ v₂

(16.5) (30) = (9) v₂

v₂ = 55 ft/s