# Application of the Steady Flow Energy Equation

## Introduction

The equation is used to determine total energy flows in open systems. There is the assumption that mass flow is constant through the system as well as equal total energy input and output. The energies include; internal, kinetic, heat, flow, potential and work. In a plant operation, fan reliability is very critical as failures often forces the all process shutdown. Good ventilation is essential to maintain a fruitful working environment. Due to the great significance of fan operation in a plant, designers are mainly concerned in installing reliable ventilation systems. However, they cover these uncertainties in the design development by adding effectiveness to fans. This paper gives a detailed discussion on a centrifugal ventilator, driven by a fan motor.

In this report, the activities carried out are meant to enable the user to embrace the knowledge of field and office measures that are necessary in efficient operation of a centrifugal fan. By carrying out various procedures in data collection, an individual will set up the necessary instruments aiming to collect data and information. Critical consideration will be based on identifying known control points of the given location as well as measuring features of the identified system. In order to achieve the desired quality of both data collection and the experiment, results from the research are taken down then compared with the anticipated expectations.

This report is segmented into various sections. The first section involves setting up a data collector and its main goal is to get familiar with data collectors and acquire the fundamental knowledge regarding the importance of correct data input. The second section of this report is about setting up the total station by using a known control point and links this to the data collector. The main goal for this section was to develop clear understanding on how to set up instruments directly in consideration to the control point. The third section was about using data collector to set up a back sight. The fourth section was evaluation of any other known control point. Section five was about creating the fundamental goal of this section was acquire knowledge and develop critical skills in the creation of an engineering site plan.

Determine the unknown Q┴˙ (as indicated in Figure 1) in magnitude and direction as the heat transfer rate in kW across the boundary.

Steady Flow Energy Equation (SFEE) is given as;

m1˙(h1+V212+Z1g) +dQdt=m2˙(h2+V222+Z2g) +dWdt.

Where

m˙=mass rate flow in kg/s, dWdt is rate of work transfer in J/s, Z is elevation from datum, dQdt is rate of heat transfer in J/s, V is velocity in m/s, and, h=specific enthalpy in J/kg.

The general interest is in the heat engine where there are the steady flow processes. Mass fluid and its properties at any specific section through the system must be constant with respect to time and uniform rate of work energy and heat transfers taking place. In order to maintain the water level in the boilers, there is an equal rate of emitted steam and that of the OUTfeed water supply pump. The furnace water must supply heat energy at an equal rate to maintain the production steam at a steady pressure under the conditions that the fluids at any section in the system must be constant with respect to time. Potential energy If the fluid is at some height Z above a given datum level, then as a result of its mass it possesses potential energy with respect to that datum. Thus, for unit mass of fluid, in the close vicinity of the earth, Potential energy = g Z ≈ 9.81 Z.

Kinetic energy A fluid in motion possesses kinetic energy. If the fluid flows with velocity C, then, for unit mass of fluid, C2 Kinetic energy = 2 c) Internal energy All fluids store energy. The store of energy within any fluid can be increased or decreased as a result of various processes carried out on or by the fluid. The energy stored within a fluid which results from the internal motion of its atoms and molecules is called its internal energy and it is usually designated by the letter U. If the internal energy of the unit mass of fluid is discussed this is then called the specific internal energy and is designated by u.

Flow or displacement energy.

In order to enter or leave the system, any entering or leaving volume of fluid must be displaced with an equal volume ahead of itself. The displacing mass must do work on the mass being displaced, since the movement of any mass can only be achieved at the expense of work. Thus, if the volume of unit mass of liquid (its specific volume) at entry is v1 and its pressure is P1, then in order to enter a system it must displace an equal specific volume v1 inside the system. Thus work to the value P1v1 is done on the specific volume inside the system by the specific volume outside the system. This work is called flow or displacement work and at entry it is energy received by the system. Similarly, at exit, in order to leave, the flow work must be done by the fluid inside the system on the fluid outside the system. Thus, if the pressure at exit, is P2 and the specific volume is v2 the equation is then, Flow or displacement work rejected = P2v2 e) Heat received or rejected During its passage through the system the fluid can have direct reception or rejection of heat energy through the system boundary. This is designated by Q. This must be taken in its algebraic sense.

Thus,

Q is positive when heat is received. Q is negative when heat is rejected. Q = 0 if heat is neither received nor rejected. f) External work done During its passage through the system the fluid can do external work or have external work done on it. This is usually designated by W. This also must be taken in its algebraic sense. Thus if, External work is done by the fluid then W is positive. External work is done on the fluid then W is negative. If no external work is done on or by the fluid, then W = 0.

The experiment illustrates some thermodynamic system into which is flowing a fluid with pressure P1, specific volume v1, specific internal energy u1 and velocity C1. The entry is at height Z1 above some datum level. In its passage through the system, external work W may be done on or by the fluid and also heat energy Q may be received or rejected by the fluid from or to the surroundings. The fluid then leaves the system with pressure P2, specific volume v2, specific internal energy u2 and velocity C2. The exit is at height Z2 above some datum level. P1 v1 W U1C1 SYSTEM ENTRY (OR CONTROL VOLUME) Z1 P2 v2 u2 C2 EXIT Z2 Q

Examine the relative importance of the right-hand terms, i.e., (h_2-h_1 ), ((C_2^2-C_1^2 ))/2, g(Z_2-Z_1 ) of the steady-flow energy equation.

The right side corresponds to the control volume it is also called General Integral Equation for energy conservation in Control volume.

The application of the principle of energy conservation to the system is, Total energy entering the system = Total energy leaving the system or, for unit mass of substance, C12 C2 gZ 1 + u1 + P1v1 + + Q = gZ 2 + u 2 + P2 v 2 + 2 + W (6.1) 2 2 This is called the steady flow energy equation. This equation is not applicable to all energy forms. In such cases, the energy forms concerned are omitted from the energy equation. In equation 6.1, it was stated that the particular combination of properties of the form, u + Pv is called specific enthalpy and is designated as h. Thus, the steady flow energy equation is written as C12 C2 gZ 1 + h1 + + Q = gZ 2 + h2 + 2 + W (6.2) 2 2 Steady flow energy equation Potential energy + Kinetic energy + Internal energy +Flow or Displacement energy+ Heat or Work.