ok for some reasons i can't get the answer for this dimensionally consistent.

1.The density of a substance is given by the equation:

ρ=70.5exp(8.27x10^-7P)

where:
ρ=Density [lbm/ft3]
P=Pressure[lbf/in2]

i) what are the units of 70.5 and 8.27x10^-7 ?
ii) calculate the density in g/cm3 for a pressure of 9.0x10^6 N/m2.
iii) derive a formula for ρ(g/cm3) as a function of P (N/m2).

Question

ok for some reasons i can't get the answer for this dimensionally consistent. 

1.The density of a substance is given by the equation: 

ρ=70.5exp(8.27x10^-7P) 

where: 
ρ=Density [lbm/ft3] 
P=Pressure[lbf/in2] 

i) what are the units of 70.5 and 8.27x10^-7 ? 
ii) calculate the density in g/cm3 for a pressure of 9.0x10^6 N/m2. 
iii) derive a formula for ρ(g/cm3) as a function of P (N/m2).

zpupster · Answer

1. Since the exponential part is dimensionless, then 70.5 must have the same unit as p which is (lbm/ft3). 2. Since the argument of the exponential function must be dimensionless, then 8.27 x 10-7 must have a unit of (in.2/lbf) which is a reciprocal to the unit of P. from here http://che31.weebly.com/uploads/3/7/4/3/3743741/lect01-unitsdimensions.pdf there are some worked examples at bottom page hope they can help you