Chemical and Thermal Processes – pressurept1jtfvisuals

Under Pressure

Under Pressure Part 1

What pressure is
How you use it
How you measure it

Under Pressure Part 2

Atmospheric Pressure
Barometric Pressure
Gauge Pressure
Absolute Pressure
Vacuum Pressure

Pressure

$\mathrm{Pressure} \equiv f_{\mathrm{normal}}/A$ , with SI units of the Pascal ( $\mathrm{Pa}$ )

$1\ \mathrm{Pa} \equiv 1\ \mathrm{N}/\mathrm{m^2}$

Other common units are the $\mathrm{Torr}$ or $\mathrm{mmHg}$ , the atmosphere $(\mathrm{atm}),$ the kilopascal $(\mathrm{kPa})$ , the $\mathrm{bar}$ , and the pound per square inch $(\mathrm{psi})$ .

$\begin{aligned} 1\ \mathrm{atm} & = 1.01325\ \mathrm{bar} = 101.325\ \mathrm{kPa} = 101325\ \mathrm{Pa} \\ & = 760\ \mathrm{Torr} \\ & = 14.6959\ \mathrm{psi} \end{aligned}$

Hydrostatic Pressure

$h$

$D$

$A = \pi D^2 / 4$

$P_0$

$\rho$

$m = \rho A h,\ F = mg$

$\Delta P = \frac{mg}{A}=\frac{\rho A h g}{A} = \rho g h$

$P = \Delta P + P_0 = \rho g h + P_0$

$P$

Some Hydrostatic Pressure Units
$\mathrm{mmHg}$
$\mathrm{inHg}$
$\mathrm{inH_2O}$
$\mathrm{ftH_2O}$
$\mathrm{mH_2O}$

Manometer

$P_1 + \rho_\mathrm{A}g(h_2+h_1)$

$= \rho_\mathrm{B}g h_1 + \rho_\mathrm{C}g h_2 + P_2$

$\Delta P = P_1 - P_2$

$= [\rho_\mathrm{B} h_1 + \rho_\mathrm{C} h_2 - \rho_\mathrm{A}(h_2+h_1)] g$

For $\rho_\mathrm{A}=\rho_\mathrm{C}$

$\Delta P= (\rho_\mathrm{B}-\rho_\mathrm{A})g h_1$

Example

$P_\mathrm{Ar} = 1.493\ \mathrm{bar},$

$T = 68\ ^\circ\mathrm{F}$

$\rho_\mathrm{benzene} = 879\ \frac{\mathrm{kg}}{\mathrm{m^3}}$

$\rho_\mathrm{Hg} = 13,546\ \frac{\mathrm{kg}}{\mathrm{m^3}}$

$P_\mathrm{atm} = 1.000\ \mathrm{atm}$

Solution

$\Delta P = \rho g h$

$P_\mathrm{atm}+ \Delta P_\mathrm{piston} + \Delta P_\mathrm{C_6H_6} = \Delta P_\mathrm{Hg} + P_\mathrm{Ar}$

$101,325\ \mathrm{Pa}+\rho_\mathrm{piston}\ g\ (20\ \mathrm{cm})+879\ \frac{\mathrm{kg}}{\mathrm{m^3}}\ g\ (19.28\ \mathrm{ft})$

$=13,546\ \frac{\mathrm{kg}}{\mathrm{m^3}}\ g\ (7.480\ \mathrm{in})+149,300\ \mathrm{Pa}$

$\implies \rho_\mathrm{piston} = 11,500\ \frac{\mathrm{kg}}{\mathrm{m^3}}=11.50\frac{\mathrm{g}}{\mathrm{cm^3}}$

Spreadsheet of Solution

The Takeaways

Pressure is the second most commonly measured process variable.
Hydrostatic pressure $= \rho g h$ .
Manometers measure $\Delta P$ ’s with hydrostatic pressure.

Under Pressure Part 1 Just The Facts

Under Pressure Part 1
Just The Facts