Introduction & Context

Selecting the correct pump type—centrifugal or positive displacement—directly affects process efficiency, energy consumption, and equipment life. Centrifugal pumps impart kinetic energy to the fluid and rely on a velocity-to-pressure conversion; they dominate low-to-medium pressure, high-flow, low-viscosity duties. Positive-displacement (PD) pumps trap fixed volumes and move them regardless of downstream pressure; they excel when viscosity rises, flow must remain nearly constant, or suction conditions are difficult. The boundary layer that develops inside the suction piping—and therefore the Net Positive Suction Head available (NPSHa)—is governed by fluid viscosity, the property responsible for shear stress and momentum diffusion.

Methodology & Formulas

  1. Boundary-layer momentum balance
    The shear stress \( \tau \) in the boundary layer is proportional to the velocity gradient and viscosity \( \mu \): \[ \tau = \mu \, \frac{\partial u}{\partial y} \] where \( u \) is the local axial velocity and \( y \) the wall-normal coordinate.
  2. Reynolds number for pipe flow
    The ratio of inertial to viscous forces sets the regime: \[ Re = \frac{\rho \, u_{\text{avg}} \, D}{\mu} \] with \( \rho \) density, \( u_{\text{avg}} \) average velocity, and \( D \) pipe diameter.
  3. Flow-regime limits
    Regime Re Range Friction Factor
    Laminar \( Re \le 2300 \) \( f = \frac{64}{Re} \)
    Transition \( 2300 \lt Re \lt 4000 \) Colebrook implicit
    Turbulent \( Re \ge 4000 \) \( \frac{1}{\sqrt{f}} = -2 \log_{10}\!\left( \frac{\varepsilon/D}{3.7} + \frac{2.51}{Re\sqrt{f}} \right) \)
  4. Viscous head loss
    Darcy-Weisbach equation for pressure drop \( \Delta p \): \[ \Delta p = f \, \frac{L}{D} \, \frac{\rho \, u_{\text{avg}}^{2}}{2} \] where \( L \) is pipe length and \( f \) the friction factor obtained from the table above.
  5. NPSH available (suction side)
    Convert pressure drop to head: \[ \text{NPSH}_{a} = \frac{p_{\text{atm}} - p_{\text{v}}}{\rho \, g} - z_{\text{s}} - h_{\text{f}} \] with \( p_{\text{v}} \) vapour pressure, \( z_{\text{s}} \) static suction lift, and \( h_{\text{f}} = \Delta p / (\rho \, g) \) viscous head loss.
  6. Pump-type selection map
    Parameter Centrifugal Preferred PD Preferred
    Viscosity \( \mu \) \( \mu \le 300 \times 10^{-3} \, \text{Pa·s} \) \( \mu \gt 300 \times 10^{-3} \, \text{Pa·s} \)
    Flow rate \( Q \) High, \( Q \gt 50 \, \text{m}^{3}\,\text{h}^{-1} \) Low-to-medium, \( Q \le 50 \, \text{m}^{3}\,\text{h}^{-1} \)
    NPSH margin \( \text{NPSH}_{a} - \text{NPSH}_{r} \ge 1 \, \text{m} \) Insensitive to NPSH margin
    Shear sensitivity Tolerates moderate shear Low shear (gentle handling)