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Mechanical Properties of Fluids — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMechanical Properties of Fluids1 Mark
Question
A tank with a square base of area $1.0 \mathrm{~m}^2$ is divided by a vertical partition in the middle. The bottom of the partition has a small-hinged door of area $20 \mathrm{~cm}^2$. The tank is filled with water in one compartment, and an acid (of relative density 1.7 ) in the other, both to a height of 4.0 m . compute the force necessary to keep the door close.
✓

Answer

Water compartment, $p=h p g=4 \times 1.0 \times 109 \times 9.8$
$=39.2 \times 10 \mathrm{~Pa}$
Acid compartment, $\mathrm{P}=\mathrm{hp}$ 's
$=4 \times 1.7 \times 103 \times 9.8$
$=66.64 \times 10 \mathrm{~Pa}$
$P^{\prime}-P=66.64 \times 103-39.2 \times 10^3$
$=27.44 \times 10^3 \mathrm{~Pa}$
$A=20 \mathrm{~cm}$
$20 \times 10^{-4} \mathrm{~m}^2$
Area, using pressure, $\mathrm{P}=\frac{\mathrm{F}}{\mathrm{A}}$
$\mathrm{F}=\mathrm{PA}$
$\mathrm{~F}=\left(20 \times 10^{-4}\right) \times\left(27.44 \times 10^3\right)$
$=54.88 \mathrm{~N}$

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