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Up: Isothermal Flow
Previous: Figures and Tables
Index
There can be several kinds of questions aside from the proof
questions^{8.6}Generally, the ``engineering'' or practical questions can be divided
into driving force (pressure difference), resistance (diameter,
friction factor, friction coefficient, etc.), and mass flow
rate questions.
In this model no questions about shock (should) exist^{8.7}.
The driving force questions deal with what should be the pressure
difference to obtain certain flow rate.
Here is an example.
Solution
If the flow was incompressible then
for known density,
, the velocity can be calculated by
utilizing
.
In incompressible flow, the density is a function of the entrance Mach
number.
The exit Mach number is not necessarily
i.e.
the flow is not choked.
First, check whether flow is choked (or even possible).
Calculating the resistance,
Utilizing the table 8.1 or the program provides






0.04331 
400.00 
20.1743 
12.5921 
0.0 
0.89446 
<>
The maximum flow rate (the limiting case) can be calculated by
utilizing the above table.
The velocity of the gas at the entrance
.
The density reads
The maximum flow rate then reads
The maximum flow rate is larger then the requested mass rate
hence the flow is not choked.
It is note worthy to mention that since the isothermal model breaks
around the choking point, the flow rate is really some what different.
It is more appropriate to assume isothermal model
hence our model is appropriate.
To solve this problem the flow rate has to be calculated as
Now combining with equation (8.40) yields
From the table (8.1) or utilizing the program
provides






0.10300 
66.6779 
8.4826 
5.3249 
0.0 
0.89567 
<>
The entrance Mach number obtained by






0.04014 
466.68 
21.7678 
13.5844 
0.0 
0.89442 
<>
The pressure should be
Note that table here above for this example are for

Solution
At first, the minimum diameter will be obtained when the flow is
choked.
Thus, the maximum
that can be obtained when the
is at
its maximum and back pressure is at the atmospheric pressure.
Now, with the value of
either utilizing Table
(8.1)
or using the provided program yields






0.08450 
94.4310 
10.0018 
6.2991 
0.0 
0.87625 
<>
With
the value of minimum diameter.
However, the pipes are provided only in 0.5 increments and the next
size is
or
.
With this pipe size the calculations are to be repeated in reversed
to produces: (Clearly the maximum mass is determined with)
The usage of the above equation clearly applied to the whole pipe.
The only point that must be emphasized is that all properties (like
Mach number, pressure and etc) have to be taken at the same point.
The new
is






0.08527 
92.6400 
9.9110 
6.2424 
0.0 
0.87627 
<>
To check whether the flow rate is satisfied the requirement
Since
the mass flow rate requirements is satisfied.
It should be noted that
should be replaced by
in the
calculations.
The speed of sound at the entrance is
and the density is
The velocity at the entrance should be
The diameter should be
Nevertheless, for sake of the exercise the other parameters will be
calculated.
This situation is reversed question.
The flow rate is given with the diameter of the pipe.
It should be noted that the flow isn't choked.

Solution
In this chapter, there are no examples on isothermal with
supersonic flow.
Next: Unchoked situations in Fanno
Up: Isothermal Flow
Previous: Figures and Tables
Index
Created by:Genick BarMeir, Ph.D.
On:
20071121
