Solutions

1 We have :-

   

 

from this we can get:-

This expression must be transferred to Mathcad and the mass flow plotted against n

The outcome is that the flow as calculated is not dependent on the value of n. This is extraordinarily convenient

 

2 From the Moody diagram  for copper =0.0015 .

Now  will be large  and then .  and we can put  (simply chosen) and then :-

.  

.    .

At this moss flow

 and a better value of  =.0045

This means that the friction term becomes  and  and

From this  which is near enough.

( Note that where the pipe is long compared with its diameter the pressure term is small compared with the friction term. In most cases of practical pneumatic transport the pressure term can be ignored and the expression much simplified.)

 

3 7.5 bar gauge = 8.5 bar absolute;  7 bar gauge = 8 bar absolute.

 and then:-

.   and :-

                                 .

 

4 8.5 bar gauge = 9.5 bar absolute;  7 bar gauge = 8 bar absolute

 and then:-

.  and