A gate in an irrigation canal is constructed in the form of a trapezoid 2 m wide at the bottom, 38 m wide at the top, and 2 m high. It is placed vertically in the canal so that the water just covers the gate. Find the hydrostatic force on one side of the gate.

Note that your answer should be in Newtons, and use g = 9.8 m/s2.

Question

Physics

Mariana Townsend

6 April, 20:18

A gate in an irrigation canal is constructed in the form of a trapezoid 2 m wide at the bottom, 38 m wide at the top, and 2 m high. It is placed vertically in the canal so that the water just covers the gate. Find the hydrostatic force on one side of the gate.

Note that your answer should be in Newtons, and use g = 9.8 m/s2.

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Answers (1)

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Maryjane Bartlett · Answer 1

Area of trapezoid = [ (2 + 38) / 2 ] x 2 = 40 sq m.

Pressure at the centre of the trapezium

= h d g = 1 x 10³ x 9.8 N / m² (height of centre is 1 m)

= 9800 N / m²

Total force required = pressure at the centre x total area

9800 x 40 = 392 x 10³ N.