# Ratio of force of water to force of oil acting on submerged plate

Date of Exam

**Problem**

A vertical rectangular plate is submerged half in oil (s = 0.8) and half in water such that its top edge is flushed with the oil surface. What is the ratio of the force exerted by water on the lower half to that by oil acting on the upper half?

A. 1.53 | C. 4.33 |

B. 2.55 | D. 3.25 |

**Answer Key**

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[ D ]

**Solution**

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$F_1 = p_{cg1} A_1$

$F_1 = [ \, 9.81(0.8)(\frac{1}{2}a) \, ](ab)$

$F_1 = 3.924a^2b$

$F_2 = p_{cg2} A_2$

$F_2 = \left[ \, 9.81(0.8)(a) + 9.81 \left( \dfrac{a}{2} \right) \, \right] (ab)$

$F_2 = 12.753a^2b$

Required ratio

$\dfrac{F_2}{F_1} = \dfrac{12.753a^2b}{3.924a^2b}$

$\dfrac{F_2}{F_1} = 3.25$ ← *answer*

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