What are the three basic assumptions when deriving the basic equation of vane pump?

suppose 1: the liquid is in a constant flow. When the impeller speed is constant, the absolute motion outside the impeller can be considered to be constant. After the pump is started for a period of time, if the external conditions remain unchanged, this assumption can basically be considered to be consistent with the reality.

assumption 2: it is assumed that the number of blades in the impeller is infinitely many and infinitely thin, which is quite different from the actual impeller. Actually, the impeller of water pump generally has 2-12 blades. In the blade slot, the water flow has a certain degree of freedom. When the impeller drives the water flow to rotate together, the water flow particles tend to keep the original position of the water flow due to the inertia, thus producing a rotating motion opposite to the rotation direction of the impeller, that is, the "counter-rotating phenomenon" of the water flow in the closed blade groove.

assumption 3: ideal liquid. Because the water delivered by the water pump has head loss when it flows through the water pump. Therefore, the actual head of the pump will always be less than its theoretical head value.