What is the Centrifugal Pump?
Centrifugal pumps are a sub-class of dynamic axisymmetric work-absorbing turbomachinery. Centrifugal pumps are used to transport fluids by the conversion of rotational kinetic energy to the hydrodynamic energy of the fluid flow. The rotational energy typically comes from an engine or electric motor. The fluid enters the pump impeller along or near to the rotating axis and is accelerated by the impeller, flowing radially outward into a diffuser or volute chamber (casing), from where it exits.
Common uses include water, sewage, petroleum and petrochemical pumping; a centrifugal fan is commonly used to implement a vacuum cleaner. The reverse function of the centrifugal pump is a water turbine converting potential energy of water pressure into mechanical rotational energy.
According to Reti, the first machine that could be characterized as a centrifugal pump was a mud lifting machine which appeared as early as 1475 in a treatise by the Italian Renaissance engineer Francesco di Giorgio Martini. True centrifugal pumps were not developed until the late 17th century, when Denis Papin built one using straight vanes. The curved vane was introduced by British inventor John Appold in 1851.
How it works
Like most pumps, a centrifugal pump converts rotational energy, often from a motor, to energy in a moving fluid. A portion of the energy goes into kinetic energy of the fluid. Fluid enters axially through eye of the casing, is caught up in the impeller blades, and is whirled tangentially and radially outward until it leaves through all circumferential parts of the impeller into the diffuser part of the casing. The fluid gains both velocity and pressure while passing through the impeller. The doughnut-shaped diffuser, or scroll, section of the casing decelerates the flow and further increases the pressure.
Description by Euler
A consequence of Newton's second law of mechanics is the conservation of the angular momentum (or the "moment of momentum") which is of fundamental significance to all turbomachines. Accordingly, the change of the angular momentum is equal to the sum of the external moments. Angular momentums ρ×Q×r×cu at inlet and outlet, an external torque M and friction moments due to shear stresses Mτ are acting on an impeller or a diffuser.
Since no pressure forces are created on cylindrical surfaces in the circumferential direction, it is possible to write Eq. (1.10) as:
Euler's pump equation
Based on Eq.(1.13) Euler developed the head pressure equation created by the impeller see Fig.2.2
In Eq. (2) the sum of 4 front element number call static pressure,the sum of last 2 element number call velocity pressure look carefully on the Fig 2.2 and the detail equation.
Ht theory head pressure ; g = between 9.78 and 9.82 m/s2 depending on latitude, conventional standard value of exactly 9.80665 m/s2 barycentric gravitational acceleration
u2=r2.ω the peripheral circumferential velocity vector
u1=r1.ω the inlet circumferential velocity vector
ω=2π.n angular velocity
w1 inlet relative velocity vector
w2 outlet relative velocity vector
c1 inlet absolute velocity vector
c2 outlet absolute velocity vector
The color triangle formed by velocity vector u,c,w called "velocity triangle". this is an important role in old academic, this rule was helpful to detail Eq.(1) become Eq.(2) and wide explained how the pump works.
Fig 2.3 (a) shows triangle velocity of forward curved vanes impeller ; Fig 2.3 (b) shows triangle velocity of radial straight vanes impeller. It illustrates rather clearly energy added to the flow (shown in vector c) inversely change upon flow rate Q (shown in vector cm).