Obtaining Formulas from Unit Considerations

A tank is filled with oil whose density is ρ = 850 kg/m³. If the volume of the tank is V = 2 m³, determine the amount of mass m in the tank.

Question

Obtaining Formulas from Unit Considerations

A tank is filled with oil whose density is ρ = 850 kg/m³. If the volume of the tank is V = 2 m³, determine the amount of mass m in the tank.

Accepted Answer

The volume of an oil tank is given. The mass of oil is to be determined.

mined.
Assumptions Oil is an incompressible substance and thus its density is constant.
Analysis A sketch of the system just described is given in Fig. 1–12. Suppose we forgot the formula that relates mass to density and volume. However,
we know that mass has the unit of kilograms. That is, whatever calculations we do, we should end up with the unit of kilograms. Putting the given information into perspective, we have

[latex] ho=850 kg / m ^{3} \quad ext { and } \quad V=2 m ^{3} [/latex]

It is obvious that we can eliminate m³ and end up with kg by multiplying these two quantities. Therefore, the formula we are looking for should be

[latex] m= ho V [/latex]

Thus,

[latex] m=\left(850 kg / m ^{3} ight)\left(2 m ^{3} ight)= 1 7 0 0 kg [/latex]

Discussion Note that this approach may not work for more complicated formulas.

Question 1.2: Obtaining Formulas from Unit Considerations A tank is filled...

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