Variation of flow properties and Mach number with duct length

Variation of flow properties

The flow properties (P,T,ρ,C)at M=M*=1are used as reference values for non-dimensionalizing various properties at any section of the duct.

Temperature

Stagnation temperature –Mach number relation

At critical state

M=1

T0 = T0*

Variation of Mach number with duct length

The duct length required for the flow to pass from a given initial mach number M1 to a given final mach number m2can be obtained from the following expression.

Mean friction coefficient with respect to duct length is given by

The distance (L) between two section of duct where the ach numbers M1 &M2 are given by

Problems

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1. Air flows through a pipe of 300 mm diameter. At inlet temperature is 35 C, pressure is 0.6 bar and stagnation pressure is 12 bar.At a location 2 m down stream, the static pressure is 0.89 bar.Estimate the average friction coefficient between two section.

2 A circular duct passes 8.25 Kg / S of air at an exit Mach number of 0.5. The entry

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pressure and temperature are 345 KPa and 38 C respectively and the co – efficient of friction 0.005. If the Mach number at entry is 0.15, determine,

(i)   The diameter of the duct,

(ii)   Length of the duct,

(iii) Pressure and temperature at exit and

(iv) Stagnation pressure loss.

Given Data:

m = 8.25 Kg / S ;   M2 = 0.5 ;  P1 =  345 KPa ; T1  = 311K ; f =0.005 ;

M1= 0.15

(i)           Diameter of the pipe

Question – 3 :- Air is flowing in an insulated duct with a Mach number of M1 = 0.25. At a section downstream the entropy is greater by amount 0.124 units, as a result of friction. What is the Mach number of this section? The static properties at inlet are 700KPa and 60⁰C. Find velocity, temperature and pressure at exit. Fin d the properties at the critical section.

Given Data: M1 = 0.25; (S2 – S1) = 0.124 KJ/ Kg K; P1 = 700 KPa; T1 = 60 +273 = 333K

We know that,