Thermodynamics Lab Report

Thermodynamics Lab Report



Table of Contents

Experiment number 012

Introduction2

Derivation of flow rate equation at choked condition2

Derivation of critical pressure ratio5

Experiment number 029

Causes of differences between experimental and theoretical values10

How to identify difference between experimental and theoretical values without measuring air flow11

Conclusions11

References12

Thermodynamics Lab Report

Experiment number 01

Introduction

Compressible appears in many natural and many technological processes. Compressible flow deals with more than air, including steam, natural gas, nitrogen and helium, etc. For instance, the flow of natural gas in a pipe system, a common method of heating in the U.S., should be considered a compressible flow. These processes include the flow of gas in the exhaust system of an internal combustion engine, and also gas turbine, a problem that led to the Fanno flow model. The above flows that were mentioned are called internal flows. Compressible flow also includes flow around bodies such as the wings of an airplane, and is considered an external flow.

Discussion

Derivation of flow rate equation at choked condition

According to the law of conservation of mass the amount of mass with in a system always remain constant. Mass is defined as the quantity of matter present in a body and mathematically it can be written as an equivalent to product of density and volume of the system. In case of fluids, such as gases and liquids the shape density and volume all can vary to large extent with respect to time and mass can travel physically from one place to another.

From the law of conservation of mass it can be concluded that the mass flow rate through a nozzle will always remain constant and is equal to the mathematical product of density ?, velocity V and flow area A which can be written as follows:

= ? x V X A -------- (1)

From the above equation it is clear that for a fixed area and constant density the mass flow rate can be increased indefinitely by increasing the velocity theoretically. However, in actual practice the density does not remain constant as the velocity is increased due to compressibility effects.

In order to account the variations in density to calculate the mass flow rate at higher velocities isentropic flow and state equations are used along it the mass flow rate equation.

By the definition of speed of sound 'a' and Mach number 'M' it can be written:

V = M x a = M x v (? x R x T) -------- (2)

Where,

? = specific heat ratio

R = gas constant

T = temperature

Substituting equation number (2) in (1) we get,

= ? x M x v (? x R x T) x A ----------- (3)

Since the equation of sate is

? = ----------------- (4)

Where, p is the pressure.

Substitute (4) in (3)

= x M x v (? x R x T) x A ----------------- (5)

Rearranging the terms,

= A x v( x M x ----------------- (6)

From the isentropic flow equations:

p = pt x ------------ (7)

Where pt is the total pressure and Tt is the total temperature. Substitute Eq (7) into Eq (6)

= A x v( x M x ------------------ (8)

Another isentropic relation gives

= (1 + ...