Chapter 6, Problem 1P

To determine

Convert the given information in the accompanying table from SI units to U.S. Customary units.

Answer to Problem 1P

The conversion of given information in the accompanying table from SI units to U.S. Customary units are tabulated as follows:

Convert from SI Units	To U.S. Customary Units
$120\frac{\text{km}}{\text{hr}}$	$74.5\frac{\text{miles}}{\text{hr}}$ and $109.3\frac{\text{ft}}{\text{s}}$
$1000\text{W}$	$3412\frac{\text{Btu}}{\text{hr}}$ and $1.341\text{hp}$
$100{\text{m}}^{\text{3}}$	$3531.348{\text{ft}}^{\text{3}}$
$80\text{kg}$	$176.4\text{lbm}$
$1000\frac{\text{kg}}{{\text{m}}^{\text{3}}}$	$62.43\frac{\text{lbm}}{{\text{ft}}^{\text{3}}}$
$900\text{N}$	$202.3\text{lbf}$
$100\text{kPa}$	$14.5\frac{\text{lbf}}{{\text{in}}^2}$
$9.81\frac{\text{m}}{{\text{s}}^2}$	$32.2\frac{\text{ft}}{{\text{s}}^2}$

Explanation of Solution

Given data:

Refer to Problem 6.1 in textbook for the accompanying table.

Formula used:

Convert hr to s,

$1\text{hr}=3600\text{s}$

Convert meter to foot,

$1\text{m}=3.2808\text{ft}$

Convert foot to inches,

$1\text{ft}=12\text{in}$

Convert mile to foot,

$1\text{mile}=5280\text{ft}$

Convert km to m,

$1\text{km}=1000\text{m}$

Convert W to $\frac{\text{ft}\cdot \text{lbf}}{\text{s}}$,

$1\text{W}=0.7375\frac{\text{ft}\cdot \text{lbf}}{\text{s}}$

Convert Btu to $\text{ft}\cdot \text{lbf}$,

$1\text{Btu}=\text{778}\text{.17}\text{ft}\cdot \text{lbf}$

Convert $\frac{\text{ft}\cdot \text{lbf}}{\text{s}}$ to hp,

$1\frac{\text{ft}\cdot \text{lbf}}{\text{s}}=\frac{1}{550}\text{hp}$

Convert $\text{kg}$ to $\text{lbm}$,

$1\text{kg}=2.2046\text{lbm}$

Convert N to $\text{lbf}$,

$1\text{N}=224.809\times {10}^{-3}\text{lbf}$

Calculation:

Case 1:

Convert the given value of SI units,

$\begin{array}{c}120\frac{\text{km}}{\text{hr}}=120\frac{\left(1000\text{m}\right)}{\text{hr}}\left[\therefore 1\text{km}=1000\text{m}\right]\\ =120000\frac{\text{m}}{\text{hr}}\end{array}$ (1)

Substitute the unit $3.2808\text{ft}$ for $1\text{m}$ in equation (1).

$\begin{array}{c}120\frac{\text{km}}{\text{hr}}=120000\frac{\left(3.2808\text{ft}\right)}{\text{hr}}\\ =\left(120000\right)\left(3.2808\frac{\text{ft}}{\text{hr}}\right)\\ =393696\frac{\text{ft}}{\text{hr}}\end{array}$ (2)

Reduce the equation as follows,

$\begin{array}{c}120\frac{\text{km}}{\text{hr}}=393696\frac{\left(\frac{1}{5280}\text{miles}\right)}{\text{hr}}\left[\therefore 1\text{ft}=\frac{1}{5280}\text{miles}\right]\\ =74.5\frac{\text{miles}}{\text{hr}}\end{array}$ (3)

Substitute the unit $3600\text{s}$ for $1\text{hr}$ in equation (2).

$\begin{array}{c}120\frac{\text{km}}{\text{hr}}=393696\frac{\text{ft}}{\left(3600\text{s}\right)}\\ =\frac{393696}{3600}\frac{\text{ft}}{\text{s}}\\ =109.3\frac{\text{ft}}{\text{s}}\end{array}$ (4)

From equation (3) and equation (4), the conversion of given value of SI units to U.S. Customary units are $74.5\frac{\text{miles}}{\text{hr}}$.and $109.3\frac{\text{ft}}{\text{s}}$.

Case 2:

Convert the given value of SI units,

$\begin{array}{c}1000\text{W}=\left(1000\right)\left(0.7375\frac{\text{ft}\cdot \text{lbf}}{\text{s}}\right)\left[\therefore 1\text{W}=0.7375\frac{\text{ft}\cdot \text{lbf}}{\text{s}}\right]\\ =737.5\frac{\text{ft}\cdot \text{lbf}}{\text{s}}\end{array}$ (5)

Reduce the equation as follows,

$\begin{array}{c}1000\text{W}=737.5\frac{\left(\frac{1}{\text{778}\text{.17}}\text{Btu}\right)}{\text{s}}\left[\therefore 1\text{ft}\cdot \text{lbf}=\frac{1}{\text{778}\text{.17}}\text{Btu}\right]\\ =0.9477\frac{\text{Btu}}{\text{s}}\end{array}$ (6)

Equation (6) becomes,

$\begin{array}{c}1000\text{W}=0.9477\frac{\text{Btu}}{\left(\frac{1}{3600}\text{hr}\right)}\left[\therefore 1\text{s}=\frac{1}{3600}\text{hr}\right]\\ =\left(0.9477\right)\left(3600\frac{\text{Btu}}{\text{hr}}\right)\\ =3412\frac{\text{Btu}}{\text{hr}}\end{array}$ (7)

Substitute the unit $\frac{1}{550}\text{hp}$ for $1\frac{\text{ft}\cdot \text{lbf}}{\text{s}}$ in equation (5).

$\begin{array}{c}1000\text{W}=737.5\times \frac{1}{550}\text{hp}\\ =1.341\text{hp}\end{array}$ (8)

From equation (7) and equation (8), the conversion of given value of SI units to U.S. Customary units are $3412\frac{\text{Btu}}{\text{hr}}$ and $1.341\text{hp}$.

Case 3:

Convert the given value of SI units,

$\begin{array}{c}100{\text{m}}^{\text{3}}=100\times {\left(3.2808\text{ft}\right)}^{\text{3}}\left[\therefore 1\text{m}=3.2808\text{ft}\right]\\ =100\times {3.2808}^3{\text{ft}}^{\text{3}}\\ =3531.348{\text{ft}}^{\text{3}}\end{array}$

Thus, the conversion of given value of SI units to U.S. Customary units is $3531.348{\text{ft}}^{\text{3}}$.

Case 4:

Convert the given value of SI units,

$\begin{array}{c}80\text{kg}=80\times 2.2046\text{lbm}\left[\therefore 1\text{kg}=2.2046\text{lbm}\right]\\ =176.4\text{lbm}\end{array}$

Thus, the conversion of given value of SI units to U.S. Customary units is $176.4\text{lbm}$.

Case 5:

Convert the given value of SI units,

$\begin{array}{c}1000\frac{\text{kg}}{{\text{m}}^{\text{3}}}=1000\times 2.2046\frac{\text{lbm}}{{\text{m}}^{\text{3}}}\left[\therefore 1\text{kg}=2.2046\text{lbm}\right]\\ =2204.6\frac{\text{lbm}}{{\text{m}}^{\text{3}}}\end{array}$ (9)

Substitute the unit $3.2808\text{ft}$ for $1\text{m}$ in equation (9).

$\begin{array}{c}1000\frac{\text{kg}}{{\text{m}}^{\text{3}}}=2204.6\frac{\text{lbm}}{{\left(3.2808\text{ft}\right)}^{\text{3}}}\\ =62.43\frac{\text{lbm}}{{\text{ft}}^{\text{3}}}\end{array}$

Thus, the conversion of given value of SI units to U.S. Customary units is $62.43\frac{\text{lbm}}{{\text{ft}}^{\text{3}}}$.

Case 6:

Convert the given value of SI units,

$\begin{array}{c}900\text{N}=900\times 224.809\times {10}^{-3}\text{lbf}\left[\therefore 1\text{N}=224.809\times {10}^{-3}\text{lbf}\right]\\ =202.3\text{lbf}\end{array}$

Thus, the conversion of given value of SI units to U.S. Customary units is $202.3\text{lbf}$.

Case 7:

Convert the given value of SI units,

$\begin{array}{c}100\text{kPa}=100\times 1000\text{Pa}\left[\therefore 1\text{kPa}=1000\text{Pa}\right]\\ =100000\text{Pa}\end{array}$ (10)

Substitute the unit $\frac{\text{N}}{{\text{m}}^2}$ for $\text{Pa}$ in equation (10).

$\begin{array}{c}100\text{kPa}=100000\frac{\text{N}}{{\text{m}}^2}\\ =100000\frac{\text{N}}{{\left(3.2808\text{ft}\right)}^2}\left[\therefore 1\text{m}=3.2808\text{ft}\right]\\ =\frac{100000}{{3.2808}^2}\frac{\text{N}}{{\text{ft}}^2}\\ =9290.53\frac{\text{N}}{{\text{ft}}^2}\end{array}$ (11)

Substitute the unit $12\text{in}$ for $1\text{ft}$ in equation (11).

$\begin{array}{c}100\text{kPa}=9290.53\frac{\text{N}}{{\left(12\text{in}\right)}^2}\\ =\frac{9290.53}{{12}^2}\frac{\left(224.809\times {10}^{-3}\text{lbf}\right)}{{\text{in}}^2}\left[\therefore 1\text{N}=224.809\times {10}^{-3}\text{lbf}\right]\\ =\frac{9290.53\times 224.809\times {10}^{-3}}{144}\frac{\text{lbf}}{{\text{in}}^2}\\ =14.5\frac{\text{lbf}}{{\text{in}}^2}\end{array}$

Thus, the conversion of given value of SI units to U.S. Customary units is $14.5\frac{\text{lbf}}{{\text{in}}^2}$.

Case 8:

Convert the given value of SI units,

$\begin{array}{c}9.81\frac{\text{m}}{{\text{s}}^2}=9.81\frac{\left(3.2808\text{ft}\right)}{{\text{s}}^2}\left[\therefore 1\text{m}=3.2808\text{ft}\right]\\ =9.81\times 3.2808\frac{\text{ft}}{{\text{s}}^2}\\ =32.2\frac{\text{ft}}{{\text{s}}^2}\end{array}$

Thus, the conversion of given value of SI units to U.S. Customary units is $32.2\frac{\text{ft}}{{\text{s}}^2}$.

Conclusion:

Hence, the conversion of given information in the accompanying table from SI units to U.S. Customary units has been explained.