Answer to Question #177294 in Calculus for ali

Question

A door is submerged 5m in water. The dimensions of the gate are 5m by 4m wide.

a) the force of the water on the door

b) the distance of the centre of pressure from the surface.

c) If the door is hinged at the bottom of the door, calculate the moment the force produces about this hinge. Use ρ = 1000 kg/m3

Answer 1

a) $F=PA=\rho hg Lw =1000 \times 5 \times 5 \times4=5000 \times 20 = 100,000 N$

b)Centroid of the triangle $=\frac{4}{3}$

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Centroid of the rectangle $=\frac{2}{1}-\frac{4}{3}= \frac{2}{3}$

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c) Moment the force produces about this hinge= Moment of force is Force x distance of the hinge from the handle

M=100,000×5=500,000Nm