Answer:
V = mRT / (d²)PM
Therefore, pressure decreases as velocity increases.
This is a hypothetical concept as the friction which causes the velocity to increases also makes the pressure decrease.
Explanation:
Given the data in the question;
we know that an ideal gas equation is;
= PM/RT --------------- let this be equation 1
P is pressure, M is molecular weight, R is universal gas constant and T is the absolute temperature.
The volumetric flow rate from the continuity equation is;
Q = AV
and A = d²
so, Q = (d²)V ---------let this be equation 2
Expression for mass m in flowrate is;
m = Q ------------------let this be equation 3
so, m = (d²)V × PM/RT
solve for V
V = mRT / (d²)PM
Therefore, pressure decreases as velocity increases.
This is a hypothetical concept as the friction which causes the velocity to increases also makes the pressure decrease.