Question

Water is retained in a 1 m wide rectangular section channel by a sluice gate that can pivot about its base, as shown to the right.

Determine the tension in the horizontal retaining cable attached to the top of the gate when the depth of water in the channel is 1.5 m. The density of water is 1000 kgm−3.

Answer 1

Answer on Question #58947-Physics-Mechanics-Relativity

Water is retained in a 1 m wide rectangular section channel by a sluice gate that can pivot about its base, as shown above. Determine the tension in the horizontal retaining cable attached to the top of the gate which is 2 m high when the depth of water in the channel is 1.5 m. The density of water is 1000 kgm$^{-3}$.

Solution

First find pressure at bottom of gate:

$$P = 10 \frac{m}{s^2} \left( \frac{1000\,kg}{m^3} \right) \cdot 1.5\,m = 15000\,Pa$$

Area of gate covered with water

$$A = 1\,m \cdot 1.5\,m = 1.5\,m^2$$

Force on gate

$$F = (15000\,Pa) \cdot 1.5\,m^2 = 22.5\,kN$$

Force acts on pressure prism at $\frac{2}{3}$ water depth = 1 m or 0.5 m from bottom.

Take sum of moments about pivot = 0.

$$(22.5\,kN) \cdot 0.5\,m - T \cdot 2\,m = 0$$ $$T = \frac{22.5\,kN}{4} = 5625\,N.$$

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