 

Rough vacuum  $11000$ mbar 
Medium vacuum  $110^{3}$ mbar 
High vacuum (HV)  $10^{3}10^{7}$ mbar 
Ultra high vacuum (UHV)  $10^{7}10^{14}$ mbar 
$$p = n k_B T$$ where $n$ is particle density
So what is the pressure in a 10L chamber containing 1 gram of $\mathrm{^4He}$ at 20$^\circ$C?
$$p = \left( \frac{ N_A \frac{\mathrm{particles}}{\mathrm{mol}} }{4 \frac{\mathrm{gr}}{\mathrm{mol}}} \times \frac{1 \mathrm{gr}}{10 \mathrm{L}} \right) k_B (293 \mathrm{K}) = \\ 60.9 \mathrm{kPa} =457 \mathrm{Torr} = 8.8 \mathrm{psi} $$
Speed = $\frac{\mathrm{Volume}}{\mathrm{Time}}$ $$S = \frac{V}{t}$$
Throughput = $\frac{\textrm{Quantity of gas}}{\mathrm{Time}}$ $$ Q = \frac{p.V}{t}$$
Continuum flow: mean free path of molecules $\lambda \ll d$ diameter of the pipe. Only in rough vacuum regime
NavierStoke equation is commonly used to understand this type of flow $$ \rho \left( \frac{\partial \mathbf{u}}{\partial t} + \mathbf{u} \cdot \nabla \mathbf{u} \right) =  \nabla \bar{p} + \mu \, \nabla^2 \mathbf u + \tfrac13 \mu \, \nabla (\nabla\cdot\mathbf{u}) + \rho\mathbf{g} $$
The ultimate reference on solving this equation is An Introduction to Fluid Dynamics by G. K. Batchelor 
Re < 500 (Laminar)  Re > 2200 (Turbulent) 
Molecular flow: $\lambda \le d$ or Kn $= \frac{\lambda}{d} > 1$
Relevant in medium to ultrahigh vacuum regimes.
For large Kn $=\frac{\lambda}{d}$ in a cylindrical pipe of length $L$ and diameter $d$
$$ Q = p\frac{dV}{dt} = \frac{\sqrt{2 \pi}}6 \Delta P \frac{d^3}{ L \sqrt{\rho}}$$Page 20
1. Rotary pumps periodically increase/decrease pumping chamber volume

2. Roots pumps were invented by Francis and Philander Roots.

3. Diaphragm pumps use a flexible membrane to compress gas.

4. Turbomolecular pumps kick gas molecules in the desired direction.

