- #1

billy k

- 2

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- TL;DR Summary
- Impeller torque per speed description

Hello there, I am trying to analyze an impeller i found at home (small one) so i can find the torque-speed graph. The thing is that i get stuck in an equation with 3 unknowns instead of 2 and i don't know what else to assume.

My approach is as follows:

I take the usual equation: ## M = \dot{m} ( u_{iφ} R_i - u_{oφ} R_o) ## where M is the torque and i assume that ## u_{rel}## (relative velocity) is tangent to the geometry (see the image). So i substitue: ## u_{iφ} = ωR_i - u_{rel,i} cos(25^o) , u_{oφ} = ωR_o - u_{rel,o} cos(21^o)##

and for the mass flow (wich by the way the inlet area and outlet area are equal by geometry) :

## \dot{m} = ρ A_i u_{rel,i} sin(25^o) = ρ A_o u_{rel,o} sin(21^o) ## which gives the relation between the relative speeds (the ω term adds nothing to mass flow).

Therefore i end up with:

## M = [2π R_i b_i u_{rel,i} sin(25^o) ]* [ ω(R_o - R_i) - u_{rel,i} ( cos(25^o) - cos(21^o) * \frac{sin(25^o)}{sin(21^o)} ] ##

The last equation has the 3 unknowns and using the Μ-ω of a motor for example i still lack an equation.

Thats my question; what is the third equation? or have i done something wrong so far?

I also want to ask if its realistic to set the inlet velocity to 0 (no whirl at entrance).

Thanks in advance.

My approach is as follows:

I take the usual equation: ## M = \dot{m} ( u_{iφ} R_i - u_{oφ} R_o) ## where M is the torque and i assume that ## u_{rel}## (relative velocity) is tangent to the geometry (see the image). So i substitue: ## u_{iφ} = ωR_i - u_{rel,i} cos(25^o) , u_{oφ} = ωR_o - u_{rel,o} cos(21^o)##

and for the mass flow (wich by the way the inlet area and outlet area are equal by geometry) :

## \dot{m} = ρ A_i u_{rel,i} sin(25^o) = ρ A_o u_{rel,o} sin(21^o) ## which gives the relation between the relative speeds (the ω term adds nothing to mass flow).

Therefore i end up with:

## M = [2π R_i b_i u_{rel,i} sin(25^o) ]* [ ω(R_o - R_i) - u_{rel,i} ( cos(25^o) - cos(21^o) * \frac{sin(25^o)}{sin(21^o)} ] ##

The last equation has the 3 unknowns and using the Μ-ω of a motor for example i still lack an equation.

Thats my question; what is the third equation? or have i done something wrong so far?

I also want to ask if its realistic to set the inlet velocity to 0 (no whirl at entrance).

Thanks in advance.