Think of a volute as a curved diffuser. The outlet from the pump is shown in the upper right of the picture. The equation is also a function of the blade angle, beta. Therefore, as volumetric flow rate increases, the pressure rise decreases. For this type of pump rotor, the Euler model predicts an increasing pressure head with increasing volumetric flow rate.
Fans are pumps with forward blading.
The solidity, f, is a geometric correction relating the rotor flow area to the total rotor area. As the volumetric flow increases, there is a large deviation from the Euler model. The picture above shows the two pressure taps for the elbow gage. These two pressure taps measure the differential pressure across the diameter of the pipe in the bend. From the Bernoulli equation normal to a streamline, the fluid velocity can be calculated from this differential pressure.