Step-by-Step Solution
Step 1
We are given the values ${\rm{200}}\;{\rm{lb}} \cdot {\rm{ft}}$, ${\rm{350}}\;{\rm{lb/f}}{{\rm{t}}^3}$ and$8\;{\rm{ft/h}}$.
We are asked toconvert the units of given values.
Step 2
(a)
To convert the unit into SI form we will use the following relation.
Since $1\;{\rm{lb}} = 4.448\,{\rm{N}}$ and $1\;{\rm{ft}} = 0.3048\;{\rm{m}}$, then\[\begin{array}{c} {\rm{200}}\;{\rm{lb}} \cdot {\rm{ft}} = \left( {200\;{\rm{lb}} \cdot {\rm{ft}}} \right)\left( {{\rm{1 lb}} \times \frac{{4.448\,{\rm{N}}}}{{1\;{\rm{lb}}}}} \right)\left( {{\rm{1 ft}} \times \frac{{0.3048\,{\rm{m}}}}{{1\;{\rm{ft}}}}} \right)\\ = 271.150\;{\rm{N}} \cdot {\rm{m}}\\ = {\rm{271}}\;{\rm{N}} \cdot {\rm{m}} \end{array}\]
Step 3
(b)
To convert the unit into SI form we will use the following relation.
Since $1\;{\rm{lb}} = 4.448\,{\rm{N}}$ and $1\;{\rm{ft}} = 0.3048\;{\rm{m}}$, then\[\begin{array}{c} {\rm{350}}\;{\rm{lb/f}}{{\rm{t}}^3} = \left( {350\;\frac{{{\rm{lb}}}}{{{\rm{f}}{{\rm{t}}^3}}}} \right)\frac{{\left( {{\rm{1 lb}} \times \frac{{4.448\,{\rm{N}}}}{{1\;{\rm{lb}}}}} \right)}}{{\left( {{\rm{1 f}}{{\rm{t}}^3} \times \frac{{{{\left( {0.3048} \right)}^3}\,{{\rm{m}}^3}}}{{1\;{\rm{f}}{{\rm{t}}^3}}}} \right)}}\\ = \left( {54977.843\;{\rm{N/}}{{\rm{m}}^3} \times \frac{{{{10}^{ – 3}}\;{\rm{kN/}}{{\rm{m}}^3}}}{{1\;{\rm{N/}}{{\rm{m}}^3}}}} \right)\\ = 54.977\;{\rm{kN/}}{{\rm{m}}^3}\\ = 55.0\;{\rm{kN/}}{{\rm{m}}^3} \end{array}\]
Step 4
(c)
To convert the unit into SI form we will use the following relation.
Since $1\;{\rm{ft}} = 304.8\,{\rm{mm}}$ and $1\;{\rm{h}} = 3600\;{\rm{s}}$, then\[\begin{array}{c} 8\;{\rm{ft/h}} = \left( {8\;\frac{{{\rm{ft}}}}{{\rm{h}}}} \right)\frac{{\left( {{\rm{1 ft}} \times \frac{{304.8\,{\rm{mm}}}}{{1\;{\rm{ft}}}}} \right)}}{{\left( {{\rm{1 h}} \times \frac{{3600\,{\rm{s}}}}{{1\;{\rm{h}}}}} \right)}}\\ = 0.677\;{\rm{mm/s}} \end{array}\]