write what you understand in this example, simple answer EXAMPLE 5–10Bernoulli Equation for Compressible FlowDerive the Bernoulli equation when the compressibility effects are not negli-gible for an ideal gas undergoing (a) an isothermal process and (b) an isen-tropic process.SOLUTION The Bernoulli equation for compressible flow is to be obtainedfor an ideal gas for isothermal and isentropic processes.Assumptions 1 The flow is steady and frictional effects are negligible. 2 Thefluid is an ideal gas, so the relation P = pRT is applicable. 3 The specificheats are constant so that Plp* = constant during an isentropic process.Analysis (a) When the compressibility effects are significant and the flowcannot be assumed to be incompressible, the Bernoulli equation is given byEq. 5-40 asdP 4 V².v?+ gz = constant(along a streamline)(1)The compressibility effects can be properly accounted for by expressing p interms of pressure, and then performing the integration S dPlp in Eq. 1. Butthis requires a relation between P and p for the process. For the isothermalexpansion or compression of an ideal gas, the integral in Eq. 1 can be per-formed easily by noting that T = constant and substituting p = PIRT. ItgivesdP= RT In PPIRTSubstituting into Eq. 1 gives the desired relation,Isothermal process:RT In P ++ gz = constant(2)(b) A more practical case of compressible flow is the isentropic flow of idealgases through equipment that involves high-speed fluid flow such as nozzles,diffusers, and the passages between turbine blades. Isentropic (i.e.,reversible and adiabatic) flow is closely approximated by these devices, andit is characterized by the relation Plp* = C = constant, where k is the spe-cific heat ratio of the gas. Solving for p from Plp* = C gives p = C-/k pl./k.Performing the integration,P- +1- 1/k + 1dP = C(3)P - 1/k + 1Substituting, the Bernoulli equation for steady, isentropic, compressible flowof an ideal gas becomesk PIsentropic flow:+ gz = constant(4a)- 1+ gz, =+ gz(4b)A common practical situation involves the acceleration of a gas from rest(stagnation conditions at state 1) with negligible change in elevation. Inthat case we have z= z, and V, = 0. Noting that p = PIRT for ideal.......

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PLE 5–10 Bernoulli Equation for Compressible Flow the Bernoulli equation when the compressibility effects are not negli- for an ideal gas undergoing (a) an isothermal process and (b) an isen- process. TION The Bernoulli equation for compressible flow is to be obtained ideal gas for isothermal and isentropic processes. ptions 1 The flow is steady and frictional effects are negligible. 2 The s an ideal gas, so the relation P = pRT is applicable. 3 The specific are constant so that Plp* = constant during an isentropic process. is (a) When the compressibility effects are significant and the flow t be assumed to be incompressible, the Bernoulli equation is given by 40 as

PLE 5–10 Bernoulli Equation for Compressible Flow the Bernoulli equation when the compressibility effects are not negli- for an ideal gas undergoing (a) an isothermal process and (b) an isen- process. TION The Bernoulli equation for compressible flow is to be obtained ideal gas for isothermal and isentropic processes. ptions 1 The flow is steady and frictional effects are negligible. 2 The s an ideal gas, so the relation P = pRT is applicable. 3 The specific are constant so that Plp* = constant during an isentropic process. is (a) When the compressibility effects are significant and the flow t be assumed to be incompressible, the Bernoulli equation is given by 40 as

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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