Pump Primer 1 $100 - 8 Hours - Technical Learning College

The Hydraulic Lever
A cylinder and piston is a chamber of variable volume, a mechanism for transforming pressure
to force.
If A is the area of the cylinder, and p the pressure of
the fluid in it, then F = pA is the force on the piston. If
the piston moves outwards a distance dx, then the
change in volume is dV = A dx.
The work done by the fluid in this displacement is dW
= F dx = pA dx = p dV. If the movement is slow enough that inertia and viscosity forces are
negligible, then hydrostatics will still be valid. A process for which this is true is called quasistatic.
Now consider two cylinders, possibly of different areas A and A', connected with each
other and filled with fluid. For simplicity, suppose that there are no gravitational forces.
Then the pressure is the same, p, in both cylinders. If the fluid is incompressible, then dV + dV'
= 0, so that dW = p dV + p dV' = F dx + F' dx' = 0. This says the work done on one piston is
equal to the work done by the other piston: the conservation of energy. The ratio of the forces
on the pistons is F' / F = A' / A, the same as the ratio of the areas, and the ratios of the
displacements dx' / dx = F / F' = A / A' is in the inverse ratio of the areas. This mechanism is the
hydrostatic analogue of the lever, and is the basis of hydraulic activation.
Bramah Hydraulic Press
The most famous application of this principle is the Bramah hydraulic press, invented by Joseph
Bramah (1748-1814), who also invented many other useful machines, including a lock and a
toilet. Now, it was not very remarkable to see the possibility of a hydraulic press; what was
remarkable was to find a way to seal the large cylinder properly.
This was the crucial problem that Bramah solved by his leather seal that was held against the
cylinder and the piston by the hydraulic pressure itself. In the presence of gravity, p' = p + ρgh,
where h is the difference in elevation of the two cylinders. Now, p' dV' = -dV (p + ρgh) =-p dV -
(ρ dV) gh, or the net work done in the process is p' dV' + p dV = -dM gh, where dM is the mass
of fluid displaced from the lower cylinder to the upper cylinder. Again, energy is conserved if we
take into account the potential energy of the fluid. Pumps are seen to fall within the province of
hydrostatics if their operation is quasi-static, which means that dynamic or inertia forces are
negligible.
Pumps
Pumps are used to move or raise fluids. They are not only very useful, but are excellent
examples of hydrostatics. Pumps are of two general types, hydrostatic or positive displacement
pumps, and pumps depending on dynamic forces, such as centrifugal pumps. Here we will only
consider positive displacement pumps, which can be understood purely by hydrostatic
considerations. They have a piston (or equivalent) moving in a closely-fitting cylinder and forces
are exerted on the fluid by motion of the piston. We have already seen an important example of
this in the hydraulic lever or hydraulic press, which we have called quasi-static.
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