Chapter 1.11, Problem 46P

To determine

Express the pressure in the compressed air storage tank in $\text{kN and m units}$, $\text{kg, m and s units}$ and $\text{kg, km and s units}$.

Answer to Problem 46P

The pressure in the compressed air storage tank in $\text{kN and m units}$, $\text{kg, m and s units}$ and $\text{kg, km and s units}$ are $1200\text{kN}/{\text{m}}^{\text{2}}$, $1,200,000\text{kg}/\text{m}\cdot {\text{s}}^{\text{2}}$ and $1,200,000,000\text{kg}/\text{km}\cdot {\text{s}}^{\text{2}}$ respectively.

Explanation of Solution

Write the expression of conversion relation for the pressure in the tank from $\text{kPa}$ to $\text{kN and m units}$.

$\begin{array}{c}P\left(\text{kPa}\right)=P\left(\text{kPa}\right)\times \frac{1\text{kN}/{\text{m}}^{\text{2}}}{1\text{kPa}}\\ =P\left(\text{kN}/{\text{m}}^{\text{2}}\right)\end{array}$

Write the expression of conversion relation for the pressure in the tank from $\text{kPa}$ to $\text{kg, m and s units}$.

$\begin{array}{c}P\left(\text{kPa}\right)=P\left(\text{kPa}\right)\times \frac{1\text{kN}/{\text{m}}^{\text{2}}}{1\text{kPa}}\times \frac{1000\text{kg}/\text{m}\cdot {\text{s}}^{\text{2}}}{1\text{kN}}\\ =P\left(\text{kg}/\text{m}\cdot {\text{s}}^{\text{2}}\right)\end{array}$

Write the expression of conversion relation for the pressure in the tank from $\text{kPa}$ to $\text{kg, km and s units}$.

$\begin{array}{c}P\left(\text{kPa}\right)=P\left(\text{kPa}\right)\times \frac{1\text{kN}/{\text{m}}^{\text{2}}}{1\text{kPa}}\times \frac{1000\text{kg}/\text{m}\cdot {\text{s}}^{\text{2}}}{1\text{kN}}\times \frac{1000\text{m}}{1\text{km}}\\ =P\left(\text{kg}/\text{km}\cdot {\text{s}}^{\text{2}}\right)\end{array}$

Conclusion:

Convert the unit of pressure in the tank from $\text{kPa}$ to $\text{kN and m units}$.

$\begin{array}{c}P=1200\text{kPa}\\ =1200\text{kPa}\times \frac{1\text{kN}/{\text{m}}^{\text{2}}}{1\text{kPa}}\\ =1200\text{kN}/{\text{m}}^{\text{2}}\end{array}$.

Convert the unit of pressure in the tank from $\text{kPa}$ to $\text{kg, m and s units}$.

$\begin{array}{c}P=1200\text{kPa}\\ =1200\text{kPa}\times \frac{1\text{kN}/{\text{m}}^{\text{2}}}{1\text{kPa}}\times \frac{1000\text{kg}/\text{m}\cdot {\text{s}}^{\text{2}}}{1\text{kN}}\\ =1,200,000\text{kg}/\text{m}\cdot {\text{s}}^{\text{2}}\end{array}$

Convert the unit of pressure in the tank from $\text{kPa}$ to $\text{kg, km and s units}$.

$\begin{array}{c}P=1200\text{kPa}\\ =1200\text{kPa}\times \frac{1\text{kN}/{\text{m}}^{\text{2}}}{1\text{kPa}}\times \frac{1000\text{kg}/\text{m}\cdot {\text{s}}^{\text{2}}}{1\text{kN}}\times \frac{1000\text{m}}{1\text{km}}\\ =1,200,000,000\text{kg}/\text{km}\cdot {\text{s}}^{\text{2}}\end{array}$

Thus, the pressure in the compressed air storage tank in $\text{kN and m units}$, $\text{kg, m and s units}$ and $\text{kg, km and s units}$ are $1200\text{kN}/{\text{m}}^{\text{2}}$, $1,200,000\text{kg}/\text{m}\cdot {\text{s}}^{\text{2}}$ and $1,200,000,000\text{kg}/\text{km}\cdot {\text{s}}^{\text{2}}$ respectively.