Using separatecylinders model, show that for turbulent flow based on Blasius equation, the value of

1
Homework 3
Using separate-cylinders model, show that for
turbulent flow based on Blasius equation, the
value of the exponent for two-phase multipliers
equation is n2.375.
Hint Refering to fluid mechanics textbooks find
and use Blasius equation for friction factor in
turbulent pipe flows when 3000ltRelt70,000
2
Homework 3
The Blasius equation is given for the friction
factor in turbulent pipe flow for 3000ltRelt70000
with slightly different factors
We had the following relations in the model. The
two-phase multiplier in the separate-cylinder
model for liquid and gas phases are also given
dp/dz is the pressure drop in the real pipe and
imaginary pipes as they are equal.
3
Homework 3
Using the Blasius equation for Cf we can write
that
This is Re for the gas flow in real pipe, which
is approximately the same in imaginary pipe
Re for the equivalent single-phase gas flow in
the real pipe.
4
Homework 3
Therefore
This represents the pressure drop for the
equivalent single-phase gas flow (-dp/dz)g
Similarly
That is n19/82.375