Answer:
The density equation is given by:
p = 70.5 * exp(82700000 * p)
where p is the pressure in pounds per square inch (lbf/in²) and ρ is the density in pounds per cubic foot (lbm/ft³).
To determine the units of the constants 70.5 and 82700000 in short, we can use dimensional analysis.
The unit of the exponential term is dimensionless, so we only need to consider the units of the constant term.
The unit of the density (ρ) is lbm/ft³, and the unit of the pressure (p) is lbf/in².
So, we can write the equation as:
ρ = (70.5 lbm/ft³) * exp(82700000 * p)
To get the units of the constant 70.5, we can divide both sides by the exponential term and simplify:
ρ / exp(82700000 * p) = 70.5 lbm/ft³
Therefore, the units of 70.5 are lbm/ft³.
To get the units of the constant 82700000, we can rearrange the equation and take the natural logarithm of both sides:
ln(ρ/70.5 lbm/ft³) = 82700000 * p
The units of the left-hand side are dimensionless, and the units of the right-hand side are 1/in². So, the units of the constant 82700000 are 1/in².