Question

Perform the following unit conversions using units of length, mass, and time only to convert. Show your work, do not just use Google.

(a) 1 L to in.3
(b) 0.135 kW to ft.·lbf./s
(c) 304 kPa to psi
(d) 122 ft.3 to m3
(e) 100 hp to kW
(f) 1000 lbm. to kg

Answer 1

Answer:

$\mathbf{1\ L=61.02384\ in^3}$

$\mathbf{0.135\ kW=99.5709185406\ ft-lb/s}$

$\mathbf{304\ kPa=44.091435811\ psi}$

$\mathbf{122\ ft^3=3.45465495258\ m^3}$

$\mathbf{100\ hp=74.6\ kW}$

$\mathbf{1000\ lbm=453.592\ kg}$

Explanation:

$1\ L=10^{-3}\ m^3$

$1\ m=39.3701\ in$

$10^{-3}\ m^3=10^{-3}\times 39.3701^3=61.02384\ in^3$

$\mathbf{1\ L=61.02384\ in^3}$

$0.135\ kW=135\ W$

$135\ W=135\ Nm/s$

$1\ N=0.224809\ lbf$

$1\ m=3.28084\ ft$

$135\times 0.224809\times 3.28084=99.5709185406\ ft-lb/s$

$\mathbf{0.135\ kW=99.5709185406\ ft-lb/s}$

$304\ kPa=304000\ N/m^2$

$1\ m=39.3701\ in$

$304000\ N/m^2=304000\times 0.224809\times \dfrac{1}{39.3701^2}=44.091435811\ psi$

$\mathbf{304\ kPa=44.091435811\ psi}$

$122\ ft^3=\dfrac{122}{3.28084^3}=3.45465495258\ m^3$

$\mathbf{122\ ft^3=3.45465495258\ m^3}$

$1\ hp=746\ W$

$100\ hp=100\times 746\ W=74.6\ kW$

$\mathbf{100\ hp=74.6\ kW}$

$1\ lbm=0.224809\ kg$

$1000\ lbm=1000\times 0.453592=453.592\ kg$

$\mathbf{1000\ lbm=453.592\ kg}$