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Physics

Fluid-Mechanics

Easy

Question

Two immiscible liquids of densities d and 2d with heights h and 2h respectively push a vertical plate as shown. If b is width of the plate, total side thrust given by liquids on the vertical plate will be

$7 d b h^{2}$
$\frac{13 d b h^{2}}{4}$
$6 d b h^{2}$
$\frac{13 d b h^{2}}{2}$

The correct answer is: $fraction numerator 13 d b h squared over denominator 2 end fraction$

Let $F subscript 1 space text and end text F subscript 2$ be the forces applied by the upper and lower liquids on the plate then F₁ = (Average Pressure) Area of upper plate
$table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell equals left parenthesis fraction numerator 0 plus d g h over denominator 2 end fraction right parenthesis b h equals fraction numerator d b h squared over denominator 2 end fraction end cell row cell F subscript 2 equals fraction numerator left parenthesis d g h plus d g h plus 4 d g h right parenthesis over denominator 2 end fraction left parenthesis 2 b h right parenthesis equals 6 d b h squared end cell row cell not stretchy rightwards double arrow F equals F subscript 1 plus F subscript 2 equals fraction numerator d b h squared over denominator 2 end fraction plus 6 d b h squared equals fraction numerator 13 d b h squared over denominator 2 end fraction end cell end table$

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