Careful!
You'll have him again asserting that it relates to pumps and vertical lift.
I gave a formula for power. The basic physics is fairly simple.
It's bad enough that you didn’t understand the origins of your own equation, but to have yourself and your cronies gloat over your mistake compounds it. So let's take a look at the origin of your equation and you tell me that it still isn't a vertical lift equation.
Let's start with the general equation for power in a pump. If you need confirmation of this, you can find it in your text books or here is a convenient
wiki-link.
P = Δp * Q / η , where:
Δp = (your D) = pressure differential
Q = (your Q) = Flow Rate
η = (your eta) = efficiency
Notice the similarity of the general equation to your equation. The only difference is the Δp. I will rewrite your equation first using your variables, and then using standard variables to conform with the standard equation.
Pi= D*g*H*Q/eta = ρ * g * H * Q / η , where:
ρ = (your D) = density
It is easy to see that
ρ*g*H = Δp and the units match as well. (kg/m
3) * (m/s
2) * (m) = (kg/m/s
2).
However, it is also quite obvious that the term (ρ*g*H) is the pressure at the bottom of a column of fluid (gas or liquid). The same wiki article confirms this
farther on.
So your Δp is the difference in pressure from the bottom of a column to the top of a column, which is in fact, a fluid lift differential. As I stated back in the beginning, your equation (which I never said was not valid) is a
"lift equation". It is valid, but does not apply to the discussion we have been engaged in.
Here is an example where your equation fails: You need to size a recirculation pump, where there is no elevation change (H=0), but the pressure differential is the result of frictional losses and other restrictions in the piping. Your Δp is the
wrong Δp for this problem.
If you had actually understood the source and nature of the equation that you have grown so accustomed to using, you would have seen that it was limited to a lift equation as soon as I originally questioned it. The fact is, you cited an equation that you didn’t fully understand.
Power is force times distance divided by time.
By the way, in this continuation of your previous quote, you missed the "dot product", which would have told you that when your acceleration (g) is vertical, the distance portion is ONLY the vertical component.
===================================
For convenience, here is your original posting:
Head times flow:
Pi= D*g*H*Q/eta
where:
Pi is the input power required (W)
D is the fluid density (kg/m3)
g is the standard acceleration of gravity (9.80665 m/s2)
H is the energy Head added to the flow (m)
Q is the flow rate (m3/s)
eta is the efficiency of the pump plant as a decimal
Typically, for centrifugal fan or pump on a variable speed drive, flow varies as the square of the speed and the pressure (head) proportionally with speed.
Thus the power varies with the cube of the speed.
