# Lab report

Topics: Fluid dynamics, Volumetric flow rate, Centrifugal pump Pages: 6 (1580 words) Published: March 28, 2014
Abstract……………………………………………………………………………………………2 Introduction………………………………………………………………………………………..2 Background………………………………………………………………………………..2 Objectives…………………………………………………………………………………2 Scope………………………………………………………………………………………3 Theory review……………………………………………………………………………………..3 Design of report…………………………………………………………………………………...5 Procedures…………………………………………………………………………………………5 Results……………………………………………………………………………………………..6 Discussion…………………………………………………………………………………………6 Conclusion………………………………………………………………………………………...7 Reference……………………………………………………………………………………….....7 Appendix…………………………………………………………………………………………..7

ABSTRACT
This experiment introduces the use of dimensionless analysis and conventionally analytical method to survey the performance of centrifugal pump. The end of this experiment points out the benefit of using the “new” method to the conventional in most practical problem, especially in the survey of turbo-machine. Also, through this experiment, students know some basic indexes to assess the efficiency of pumps used. We will that for the specific fan conducting this experiment, the best efficiency point occurs at CQ = 0.2, the specific speed NS ~1.23. INTRODUCTION

Background
A fan is a turbo-machine in which work is done to increase the total pressure of the fluid leaving the device. This is achieved by a rotor or impeller, which is driven by an external source of power to move a row of blades so as to impart energy to the fluid. A centrifugal fan, the focus of this experiment, consists basically of three components: an air inlet duct, an impeller and a volute casing. The inlet duct conducts the fluid (in this case, it is air) into the impeller. The air then passes through a rotating row of blades resulting in the increase in pressure and velocity. The high velocity of the air in the exit of the impeller is converted into additional pressure rise by velocity reduction in the volute which acts basically as a fluid collection channel. The air at higher pressure is then delivered through the outlet duct and is finally discharged into a chamber or the atmosphere. (About a centrifugal fan and the volute: please see the illustrating figures at the appendix.) A large number of variables are usually involved in characterizing the fan performance. Dimensional analysis is often used to reduce the number of variables to manageable number of dimensionless groups. This method offers an economy in characterization of the performance of turbo-machine (e.g. a fan) in terms of a few numbers of non-dimensional groups. In addition to this, dimensional analysis (applied through the concepts of similitude and modeling) also enables the prediction of the performance of turbo-machine by conducting tests on a scaled model at different operating variables e.g. rotational speed and fluid density. Objectives

To determine the relationship between pressure rise and flow rate to characterize the performance of a centrifugal fan at different rotational speed using dimensional analysis. To use the dimensionless performance characteristic curves of the scale model to make estimates of physical quantities relevant to a geometrically similar prototype fan unit.

Scope
This experiment is conducted to show only some basic applications and advantages of the dimensional analysis on a centrifugal forward curved impeller. Deeper understanding of both this analysis method and other turbo-machines are not required. THEORY REVIEW

Application of dimensional analysis to characterize fan performance The important parameters which describe the performance characteristics of a fan are the pressure rise, flow rate and input power. The fan performance is also determined by the following geometrical and operating variables: fluid density, rotational speed, impeller diameter and viscosity of the fluid. The functional relationship can be express as:

Using ω, ρ, D as repeating variables and applying Buckingham π-theorem (see...

References: 1. http://en.wikipedia.org/wiki/Volute_(pump)
2. B.R Muson, D.F Young and T.H Okiishi, Fundamentals of Fluid Mechanics, Wiley, New York (2010) - Chapter 7 and 12.
APPENDIX
1. The Buckingham π theorem:
If an equation involving k variables is dimensionally homogeneous, it can be reduced to a relationship among k-r independent dimensionless products, where r is the minimum number of reference dimensions required to describe the variables.
2. Centrifugal fan and volute image:
3. Approximated Reynolds numbers of fan at 2103 RPM and almost the same air’s condition.( Our real condition: T = 27.80 oC, Patm = 758.79 mmHg, ρatm = 1.169 kg/m3). Meanwhile, at T = 300K, P = 100kPa, ρ= 1.161 kg/m3, μ = 18.6 x 10-6 Pa.s. We have ω ~ 220 rad/s, D ~ 0.140 m.
Re = 2.692x105.