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 kg/m3\mathrm { kg } / \mathrm { m } ^ { 3 }. (b) R=40 cm, h=100 cm, p=1000 kg/m3\mathrm { kg } / \mathrm { m } ^ { 3 }. (c) R=50 cm, h=100 cm, p=800 kg/m3\mathrm { kg } / \mathrm { m } ^ { 3 }. (d) R=50 cm, h=80 cm, p=800 kg/m3\mathrm { kg } / \mathrm { m } ^ { 3 }. (e) R=50 cm, h=125 cm, p=800 kg/m3\mathrm { kg } / \mathrm { m } ^ { 3 }.

Solution

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Answered 11 months ago
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Given:

1st drum \,\rightarrow\, RaR_{a} = 40 cm40\text{ cm} ; hah_{a} = 80 cm80\text{ cm} ; ρa\rho_{a} = 1000 kg/m31000\text{ kg/m}^{3}

2nd drum \,\rightarrow\, RbR_{b} = 40 cm40\text{ cm} ; hbh_{b} = 100 cm100\text{ cm} ; ρb\rho_{b} = 1000 kg/m31000\text{ kg/m}^{3}

3rd drum \,\rightarrow\, RcR_{c} = 50 cm50\text{ cm} ; hch_{c} = 100 cm100\text{ cm} ; ρc\rho_{c} = 800 kg/m3800\text{ kg/m}^{3}

4th drum \,\rightarrow\, RdR_{d} = 50 cm50\text{ cm} ; hdh_{d} = 80 cm80\text{ cm} ; ρd\rho_{d} = 800 kg/m3800\text{ kg/m}^{3}

5th drum \,\rightarrow\, ReR_{e} = 50 cm50\text{ cm} ; heh_{e} = 125 cm125\text{ cm} ; ρe\rho_{e} = 800 kg/m3800\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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