Density of water in ft³/lb
The keyword density of water ft3/lb uses units of volume per mass, so it refers to specific volume rather than mass density.
Two reciprocal quantities
Density \( \rho \) is mass per volume, while specific volume \( v \) is volume per mass.
\[ \rho=\frac{m}{V}\quad\text{and}\quad v=\frac{V}{m}=\frac{1}{\rho} \]Therefore, if a value is needed in \( \text{ft}^3/\text{lb} \), compute \( v \) by taking the reciprocal of \( \rho \) in \( \text{lb}/\text{ft}^3 \).
Step-by-step: converting water’s density into ft³/lb
- Choose a temperature assumption because water density depends slightly on temperature.
- Use a standard reference value for density in SI units (common reference: near \(4^\circ\text{C}\), \( \rho \approx 1000\ \text{kg/m}^3 \)).
- Convert \( \text{kg/m}^3 \) to \( \text{lb}/\text{ft}^3 \) using unit factors.
- Invert the result to obtain \( v \) in \( \text{ft}^3/\text{lb} \).
Worked conversion (near 4°C)
Using the common reference \( \rho \approx 1000\ \text{kg/m}^3 \) near \(4^\circ\text{C}\) and the conversion factors \(1\ \text{kg}=2.2046226\ \text{lb}\) and \(1\ \text{m}^3=35.3146667\ \text{ft}^3\):
\[ \rho=\left(1000\ \frac{\text{kg}}{\text{m}^3}\right)\cdot\left(\frac{2.2046226\ \text{lb}}{1\ \text{kg}}\right)\cdot\left(\frac{1\ \text{m}^3}{35.3146667\ \text{ft}^3}\right) =62.4279606\ \frac{\text{lb}}{\text{ft}^3} \]Specific volume (the quantity in \( \text{ft}^3/\text{lb} \)) is the reciprocal:
\[ v=\frac{1}{\rho}=\frac{1}{62.4279606\ \text{lb}/\text{ft}^3}=0.01601846\ \frac{\text{ft}^3}{\text{lb}} \]Rounded engineering form: \( \rho \approx 62.43\ \text{lb}/\text{ft}^3 \) and \( v \approx 0.01602\ \text{ft}^3/\text{lb} \).
Quick reference values (temperature dependence)
| Condition (assumption) | Density \( \rho \) (lb/ft3) | Specific volume \( v=1/\rho \) (ft3/lb) | Interpretation |
|---|---|---|---|
| Near \(4^\circ\text{C}\) (maximum density approximation) | \(62.43\) | \(0.01602\) | \(1\ \text{ft}^3\) of water has mass \(\approx 62.4\ \text{lb}\) |
| Near \(20^\circ\text{C}\) (room temperature approximation) | \(62.32\) | \(0.01605\) | \(1\ \text{lb}\) of water occupies \(\approx 0.016\ \text{ft}^3\) |
Visualization: reciprocal relationship between lb/ft³ and ft³/lb
Final result
For water near \(4^\circ\text{C}\): \( \rho \approx 62.43\ \text{lb}/\text{ft}^3 \), so \( v=\frac{1}{\rho}\approx 0.01602\ \text{ft}^3/\text{lb} \).