Question

# Each of five cylindrical drums with radius R is filled to a height h above the bottom with a liquid of density p. Rank the drums in order of the pressure at the bottom of the drum, largest to smallest. (a) R=40 cm, h=80 cm, p=1000 $\mathrm { kg } / \mathrm { m } ^ { 3 }$. (b) R=40 cm, h=100 cm, p=1000 $\mathrm { kg } / \mathrm { m } ^ { 3 }$. (c) R=50 cm, h=100 cm, p=800 $\mathrm { kg } / \mathrm { m } ^ { 3 }$. (d) R=50 cm, h=80 cm, p=800 $\mathrm { kg } / \mathrm { m } ^ { 3 }$. (e) R=50 cm, h=125 cm, p=800 $\mathrm { kg } / \mathrm { m } ^ { 3 }$.

Solution

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Given:

1st drum $\,\rightarrow\,$ $R_{a}$ = $40\text{ cm}$ ; $h_{a}$ = $80\text{ cm}$ ; $\rho_{a}$ = $1000\text{ kg/m}^{3}$

2nd drum $\,\rightarrow\,$ $R_{b}$ = $40\text{ cm}$ ; $h_{b}$ = $100\text{ cm}$ ; $\rho_{b}$ = $1000\text{ kg/m}^{3}$

3rd drum $\,\rightarrow\,$ $R_{c}$ = $50\text{ cm}$ ; $h_{c}$ = $100\text{ cm}$ ; $\rho_{c}$ = $800\text{ kg/m}^{3}$

4th drum $\,\rightarrow\,$ $R_{d}$ = $50\text{ cm}$ ; $h_{d}$ = $80\text{ cm}$ ; $\rho_{d}$ = $800\text{ kg/m}^{3}$

5th drum $\,\rightarrow\,$ $R_{e}$ = $50\text{ cm}$ ; $h_{e}$ = $125\text{ cm}$ ; $\rho_{e}$ = $800\text{ kg/m}^{3}$

We have five cylindrical drums with their individual radii given. The drums are filled at a known height from the bottom with a liquid and we also know the densities of the liquids. We are asked to rank the cylinders in a descending order based on the pressure at their bottom.

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