A HIGH PRESSURE, LOW VOLUME, HYDRODYNAMIC PUMP COMPRISING A SLEEVE, A SHAFT ROTATABLE WITHIN THE SLEEVE, MEANS TO VARY THE GAP BETWEEN THE SHAFT AND THE SLEEVE, AND AN OUTLET IN THE SLEEVE. WHEN SUBMERGED IN OR OTHERWISE PROVIDED WITH A SUPPLY OF FLUID SUCH AS OIL, RELATIVE MOTION BETWEEN THE SLEEVE AND THE SHAFT RESULTS IN THE ESTABLISHMENT OF A HYDRODYNAMIC PRESSURE BETWEEN THE SLEEVE AND THE SHAFT WHICH PRESSURE CAN BE INCREASED OR DECREASED BY DECREASING OR INCREASING THE GAP BETWEEN THE SLEEVE AND THE SHAFT.