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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.

**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**

0

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

0

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 60^{0}C. 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,

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