Chapter 6, Problem 2P

To determine

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

Answer to Problem 2P

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

Convert from U.S. Customary Units	To SI Units
$65\frac{\text{miles}}{\text{hr}}$	$104.6\frac{\text{km}}{\text{hr}}$ and $29\frac{\text{m}}{\text{s}}$
$60000\frac{\text{Btu}}{\text{hr}}$	$1760\text{W}$
$120\frac{{\text{lb}}_{\text{m}}}{{\text{ft}}^{\text{3}}}$	$1922.25\frac{\text{kg}}{{\text{ft}}^{\text{3}}}$
$30\frac{{\text{lb}}_{\text{f}}}{{\text{in}}^2}$	$206.8\text{kPa}$
$200{\text{lb}}_{\text{m}}$	$90.7\text{kg}$
$200{\text{lb}}_{\text{f}}$	$890\text{N}$

Explanation of Solution

Given data:

Refer to Problem 6.2 in textbook for the accompanying table.

Formula used:

Convert hr to s,

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

Convert foot to meter,

$1\text{ft}=0.3048\text{m}$

Convert inches to foot,

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

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

$1\text{lbm}=0.4536\text{kg}$

Convert $\text{lbf}$ to N,

$1\text{lbf}=4.448\text{N}$

Calculation:

Case 1:

Convert the given value of U.S. Customary units,

$\begin{array}{c}65\frac{\text{miles}}{\text{hr}}=65\frac{\left(5280\text{ft}\right)}{\text{hr}}\left[\therefore 1\text{mile}=5280\text{ft}\right]\\ =343200\frac{\text{ft}}{\text{hr}}\end{array}$ (1)

Substitute the unit $0.3048\text{m}$ for $1\text{ft}$ in equation (1).

$\begin{array}{c}65\frac{\text{miles}}{\text{hr}}=343200\frac{\left(0.3048\text{m}\right)}{\text{hr}}\\ =343200\times 0.3048\frac{\text{m}}{\text{hr}}\\ =104607.36\frac{\text{m}}{\text{hr}}\end{array}$ (2)

Reduce the equation as follows,

$\begin{array}{c}65\frac{\text{miles}}{\text{hr}}=104607.36\frac{\left(\frac{1}{1000}\text{km}\right)}{\text{hr}}\left[\therefore 1\text{m}=\frac{1}{1000}\text{km}\right]\\ =104.6\frac{\text{km}}{\text{hr}}\end{array}$ (3)

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

$\begin{array}{c}65\frac{\text{miles}}{\text{hr}}=104607.36\frac{\text{m}}{\left(3600\text{s}\right)}\\ =\frac{104607.36}{3600}\frac{\text{m}}{\text{s}}\\ =29\frac{\text{m}}{\text{s}}\end{array}$ (4)

From equation (3) and equation (4), the conversion of given value of U.S. Customary units to SI units are $104.6\frac{\text{km}}{\text{hr}}$.and $29\frac{\text{m}}{\text{s}}$.

Case 2:

Convert the given value of U.S. Customary units,

$\begin{array}{c}60000\frac{\text{Btu}}{\text{hr}}=60000\frac{\left(\text{778}\text{.17}\text{ft}\cdot \text{lbf}\right)}{\text{hr}}\left[\therefore 1\text{Btu}=\text{778}\text{.17}\text{ft}\cdot \text{lbf}\right]\\ =60000\times \text{778}\text{.17}\frac{\text{ft}\cdot \text{lbf}}{\text{hr}}\\ =46690200\frac{\text{ft}\cdot \text{lbf}}{\left(3600\text{s}\right)}\left[\therefore 1\text{hr}=3600\text{s}\right]\\ =12969.5\frac{\text{ft}\cdot \text{lbf}}{\text{s}}\end{array}$

Reduce the equation as follows,

$\begin{array}{c}60000\frac{\text{Btu}}{\text{hr}}=12969.5\times \frac{1}{0.7375}\text{W}\left[\therefore 1\frac{\text{ft}\cdot \text{lbf}}{\text{s}}=\frac{1}{0.7375}\text{W}\right]\\ =17585.763\text{W}\end{array}$ (5)

From equation (5), the conversion of given value of U.S. Customary units to SI units is $17585.763\text{W}$.

Case 3:

Convert the given value of U.S. Customary units,

$\begin{array}{c}120\frac{\text{lbm}}{{\text{ft}}^{\text{3}}}=120\frac{\left(0.4536\text{kg}\right)}{{\text{ft}}^{\text{3}}}\left[\therefore 1\text{lbm}=0.4536\text{kg}\right]\\ =120\times 0.4536\frac{\text{kg}}{{\text{ft}}^{\text{3}}}\\ =54.432\frac{\text{kg}}{{\text{ft}}^{\text{3}}}\end{array}$ (6)

Substitute the unit $0.3048\text{m}$ for $1\text{ft}$ in equation (6).

$\begin{array}{c}120\frac{\text{lbm}}{{\text{ft}}^{\text{3}}}=54.432\frac{\text{kg}}{{\left(0.3048\text{m}\right)}^{\text{3}}}\\ =\frac{54.432}{{0.3048}^3}\frac{\text{kg}}{{\text{ft}}^{\text{3}}}\\ =1922.25\frac{\text{kg}}{{\text{ft}}^{\text{3}}}\end{array}$ (7)

From equation (7), the conversion of given value of U.S. Customary units to SI units is $1922.25\frac{\text{kg}}{{\text{ft}}^{\text{3}}}$.

Case 4:

Convert the given value of U.S. Customary units,

$\begin{array}{c}30\frac{\text{lbf}}{{\text{in}}^2}=30\frac{\left(4.448\text{N}\right)}{{\text{in}}^2}\left[\therefore 1\text{lbf}=4.448\text{N}\right]\\ =133.44\frac{\text{N}}{{\left(\frac{1}{12}\text{ft}\right)}^2}\left[\therefore 1\text{in}=\frac{1}{12}\text{ft}\right]\\ =133.44\times {12}^2\frac{\text{N}}{{\text{ft}}^2}\\ =19215.36\frac{\text{N}}{{\text{ft}}^2}\end{array}$ (8)

Substitute the unit $0.3048\text{m}$ for $1\text{ft}$ in equation (8).

$\begin{array}{c}30\frac{\text{lbf}}{{\text{in}}^2}=19215.36\frac{\text{N}}{{\left(0.3048\text{m}\right)}^2}\\ =\frac{19215.36}{{0.3048}^2}\frac{\text{N}}{{\text{m}}^2}\\ =206832.414\frac{\text{N}}{{\text{m}}^2}\end{array}$ (9)

Substitute the unit $\text{Pa}$ for $\frac{\text{N}}{{\text{m}}^2}$ in equation (9).

$\begin{array}{c}30\frac{\text{lbf}}{{\text{in}}^2}=206832.414\text{Pa}\\ =206832.414\times \frac{1}{1000}\text{kPa}\left[\therefore 1\text{Pa}=\frac{1}{1000}\text{kPa}\right]\\ =206.8\text{kPa}\end{array}$ (10)

From equation (10), the conversion of given value of U.S. Customary units to SI units is $206.8\text{kPa}$.

Case 5:

Convert the given value of U.S. Customary units,

$\begin{array}{c}200\text{lbm}=200\times 0.4536\text{kg}\left[1\text{lbm}=0.4536\text{kg}\right]\\ =90.7\text{kg}\end{array}$ (11)

From equation (11), the conversion of given value of U.S. Customary units to SI units is $90.7\text{kg}$.

Case 6:

Convert the given value of U.S. Customary units,

$\begin{array}{c}200\text{lbf}=200\times 4.448\text{N}\left[\because 1\text{lbf}=4.448\text{N}\right]\\ =890\text{N}\end{array}$ (12)

From equation (12), the conversion of given value of U.S. Customary units to SI units is $890\text{N}$.

Conclusion:

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