# Solving Impeller Analysis: 3 Unknowns & 0 Inlet Velocity?

• billy k
In summary, the conversation discusses the process of analyzing a pump impeller and finding the torque-speed graph. The speaker shares their approach, which involves using equations with three unknowns. They also mention using the Μ-ω equation for a motor but still needing a third equation. The conversation ends with the speaker questioning the possibility of setting the inlet velocity to 0 and recommending a book for further analysis.
billy k
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).

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Not to nitpick, but pump torque is heavily dependent on flow in addition to speed. If you really want to do a theoretical analysis of a pump impeller, get a copy of Centrifugal and Axial Flow Pumps, by A. J. Stepanoff. If you don't want to buy it, borrow a copy by interlibrary loan.

I have a copy, I read it, and I convinced myself that I do not ever want to do a theoretical analysis of a pump. Especially since it is so much easier to find the pump curve for a similar pump, then extrapolate using the pump similarity equations.

Asymptotic and berkeman

## 1. What is the purpose of solving impeller analysis with 3 unknowns and 0 inlet velocity?

The purpose of solving impeller analysis with 3 unknowns and 0 inlet velocity is to determine the performance of an impeller in a fluid flow system. This analysis helps in understanding the flow patterns, pressure distribution, and efficiency of the impeller, which are crucial for its design and optimization.

## 2. What are the 3 unknowns in impeller analysis?

The 3 unknowns in impeller analysis are the flow rate, pressure, and velocity at the outlet of the impeller. These variables are essential for calculating the performance of the impeller and understanding its behavior in a fluid flow system.

## 3. How is the impeller analysis with 3 unknowns and 0 inlet velocity solved?

The impeller analysis with 3 unknowns and 0 inlet velocity is solved using the continuity equation, Bernoulli's equation, and the Euler equation. These equations are applied to the fluid flow system to determine the unknown variables and analyze the performance of the impeller.

## 4. What are the assumptions made in solving impeller analysis with 3 unknowns and 0 inlet velocity?

The assumptions made in solving impeller analysis with 3 unknowns and 0 inlet velocity include steady flow, incompressible fluid, and negligible losses due to friction. These assumptions simplify the analysis and provide accurate results for the performance of the impeller.

## 5. What are the applications of impeller analysis with 3 unknowns and 0 inlet velocity?

The applications of impeller analysis with 3 unknowns and 0 inlet velocity include designing and optimizing impellers for various fluid flow systems, such as pumps, turbines, and compressors. This analysis is also used in the development of new impeller designs and improving the efficiency of existing ones.

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