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

`\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}`

Step-by-step explanation:

`1\ L=10^(-3)\ m^3`

`1\ m=39.3701\ in`

`10^(-3)\ m^3=10^(-3)* 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* 0.224809* 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* 0.224809* (1)/(39.3701^2)=44.091435811\ psi`

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

`122\ ft^3=(122)/(3.28084^3)=3.45465495258\ m^3`

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

`1\ hp=746\ W`

`100\ hp=100* 746\ W=74.6\ kW`

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

`1\ lbm=0.224809\ kg`

`1000\ lbm=1000* 0.453592=453.592\ kg`

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