Question
Asked Sep 12, 2019
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A 3-m wide, 8-m high, rectangular gate is located at the end of a rectangular passage that is connected to a large open tank filled with water as shown below. The gate is hinged at its bottom and held closed by a horizontal force, FH, located at the center of the gate. The maximum value for FH is 3500 kN. (a) Determine the maximum water depth, h, above the center of the gate that can exist without the gate opening, (b) Is the answer the same if the gate is hinged at the top? Explain your answer. [Answer in units of ft. for part (a)]
4 m
4 m
Hinge
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4 m 4 m Hinge

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Expert Answer

Step 1

 

Rectangular tank with gate filled with water is shown below and  values are mentioned below

 hC is position of centroid og gate from free surface and-

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figure.1 h 4 m Gate Width (B 3m Height (D 8m F 3500kN

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Step 2

When gate is hinged at bottom then moment at H would be zero because moment at hinge point is always zero i.e.,

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ΣΜ-0 so that -FX4+Fx0 4FHyF ..eqn (1)

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Step 3

Now, calculating FR and relation between h and hCP ...

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hcP 4 m FH FR figure.2 н FRyhA kN 9.81 h(3x8)here,h-h) (235.44h)kN and forrectangular section IcG hCPh BD3 h_A 12 3x83 12 hoр h+ h(3x8)

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