This is just for fun. from fluid dynamics
water is a fluid, like air, the equation holds for air, water, any fluid
Vr is velocity relative to the blade, so Vnozzle - Vblade = Vrelative
The equation setup to find the Force on the blade inside a control volume from knowing the mass flow rate and relative velocity of the fluid to the blade.
To find the force on the blade what we need is the velocity of fluid leaving the nozzle, velocity of the blade, mass flow through the turbine, area of nozzle, density of fluid and angle of the blade.
Force on the blade is equal to the difference of (mass flow times velocity)out - (mass flow times velocity)in.
mass flow is density of fluid times volume flow rate.
mass flow is also density times velocity times area.
Since mass flow out = mass flow in, all that is changing is the velocity of the fluid when it strikes the blade and redirects with some angle, which causes a force on the blade that we are interested in.
On the left hand side we convert mass flow into (density * area * velocity) and factor it out, leaving one more velocity inside the ( ) allowing us to deal with the difference in relative velocity of the stream of fluid by taking the cosine of the angle where it strikes the blade (angle is given as a variable alpha).
This example also shows how we can neglect negligible information for control situation, such as the influence of gravity and change in velocity due to volume, and some surface forces that don't need to be considered in this example. And how important mass flow is for our calculations of moving fluids, how we can use mass flow in so many different ways to make life easy when trying to figure out what will happen with fluid systems. If we have mass flow then technically we have the fluid density, velocity, and area it is flowing through, which is a lot of useful information packed into 1 term. So for example if the area is changing, we can find new velocity and density depending how we setup the equation.
https://www.grc.nasa.gov/www/k-12/airplane/mflow.html