Answer:
M = ρ*[tex]\frac{\pi }{4}[/tex]*D²*V
Explanation:
The mass flow rate (M) is the mass (m) that is flowing by a determine period, thus is the mass divided by the time (t):
[tex]M = \frac{m}{t}[/tex]
The density (ρ) of a substance is its mass divided by its volume (Vol), thus:
ρ = [tex]\frac{m}{Vol}[/tex]
m = ρ*Vol
So, the mass flow rate is:
M = ρ*Vol/t
The volume of the substance is occupying is the area (A) multiplied by the legth of the turbine (l):
Vol = A*l
M = ρ*A*l/t
And, the division of the length by the time is the velocity (V) of the fluid in the turbine, so:
M = ρ*A*V
If the turbine is a circunfernce, the area is related to its diameter (D):
A = π*D²/4
So:
M = ρ*[tex]\frac{\pi }{4}[/tex]*D²*V
