Given:
A problem in my thermodynamics text reads as follows...
A vacuum gauge connected to a tank reads $5.4\cdot psi$ at a location where the barometric reading $P_{Hg}= 28.5\cdot in$. Determine the absolute pressure in the tank. Take $\rho_{Hg} = 848.4\frac{lbm}{ft^3}$.
My Solution:
The formula for a vacuum gauge is as follows...
$$P_{vac}=P_{atm}-P_{abs}$$
Rewrite as...
$$P_{abs}=P_{atm}-P_{vac}$$
Determine atmospheric pressure but first convert $ft$ units to $in$ since that is how we traditionally define pressures in English units...
$$P_{atm}=\rho g h$$
$$\rho=848.4\cdot\frac{lbm}{ft^3}\times\frac{ft^3}{(12in)^3}=.4910\cdot\frac{lbm}{in^3}$$
$$g=32.174\cdot\frac{ft}{s^2}\times\frac{12in}{ft}=386.0\cdot\frac{in}{s^2}$$
$$P_{atm}=.4910\cdot\frac{lbm}{in^3}\times386.0\cdot\frac{in}{s^2}\times28.5\cdot in=5402\cdot\frac{lbm}{in\cdot s^2}$$
Question:
The atmospheric pressure obtained cannot be right because the scalar value $5402$ is no where near $14.7$ and the units obtained ($\frac{lbm}{in\cdot s^2}$) look completely wrong. Shouldn't they be $\frac{lbf}{in^2}$? Where did I go wrong? After this is solved I know how to obtain the absolute pressure in the tank so I shall stop here.
