Page 168 - 48Fundamentals of Compressible Fluid Mechanics

130 CHAPTER 8. ISOTHERMAL FLOW
8.7 Examples

6
There can be several kind of questions aside the proof questions Generally, the
“engineering” or practical questions can be divided into driving force (pressure dif-
ference), resistance (diameter, friction factor, friction coefficient, etc.), and mass
7
flow rate questions. In this model no questions about shock (should) exist .
The driving force questions deal with what should be the pressure differ-
ence to obtain certain flow rate. Here is an example.

Example 8.1:
A tube of 0.25 [m] diameter and 5000 [m] in length is attached to a pump. What
will be achieved.
. The specific
should be the pump pressure so that a flow rate of 2 1
. Hint
calculate the maximum flow rate and then check if this request is reasonable.

SOLUTION %!
Assume that friction factor
and the exit pressure is
If the flow was incompressible then for known density, , the velocity can be calcu-

,
heat for the gas,
, surroundings temperature ('
. In incompressible flow, the density is a function of

i.e. the

lated by utilizing
flow is not choked. First, check whether flow is choked (or even possible).
the entrance Mach number. The exit Mach number is not necessarily

Calculating the resistance,

'
Utilizing the table 8.1 or the program provides

#

The maximum flow rate (the limiting case) can be calculated by utilizing

. The density reads #

/(

% 3

(
the above table. The velocity of the gas at the entrance

"

# #
The maximum flow rate then reads

/(

3

#

6
# #
#
3 3

The proof questions are questions that ask for proof for finding a mathematical intently (normally

good for mathematicians). These questions or example will be in later versions. 1
7 Those who are mathematically include these kind of questions can exit but there is no real world
situations with isothermal model with shock.