(Presumably) simple fluids problem

[ghiggins]

I am trying to figure out the pressure change in a compressed air line. If I've got 120psi air in a 1/4"ID tube regulated to 800scfh and I change the tube size after a gauge or fitting, to a 1/2"ID tube, what is the pressure of the air being delivered at the end of the 1/2"ID tube?

Assume that there is no elevation difference and the total length is so small that there are negligible major losses.

2. Homework Equations :
3. The Attempt at a Solution :
P_1=120 psi
v_1=(800scfh*64/(pi))=2,346,835 ft/hr=651.9 ft/s=7822.8 in/s
rho_1=0.700 lb/ft^3=4.051e-4 lb/in^3 (120psig, 60F)

v_2= 163 ft/s=1956 in/s

Assume that the transition area causes negligible losses (probably very inaccurate).

Then the equation can reduce to :
[P_1/(rho_1)g]+[((v_1)^2/2g)]=[P_2/(rho_2)g]+[((v_2)^2/2g)]

Assume a value for density at 2 and iterate until they're the same.

Using rho_2=0.544 lb/ft^3=3.148e-4 lb/in^3 (density of air at 90psig, 60F), gives 9123psi at location 2. That is the pressure increased (substantially). Is the problem that I'm not accounting for minor loss at the diameter change from the valve/ tube transition?


Side Question:
Also, I never understood why, if velocity is increased the pressure of the fluid drops. If there is a decrease in the size of the hose or pipe carrying your fluid, ie: throttling, so the fluid velocity increases, it only seems reasonable that the pressure of the fluid increases. If fluid is traveling from one tube to another in series, the flow rate cannot change, so the same amount of fluid is being packed into a smaller area, obviously traveling at higher velocity. Makes you think it will become pressurized, right?

Thanks for any help and responses on this topic.

 

[Valkarie]

The pressure of the fluid drops when velocity increases because the kinetic energy of the fluid is converted to potential energy. This means that the pressure (which is the sum of potential and kinetic energies due to Bernoulli's equation) decreases. As the fluid passes through a restriction, the velocity increases and the pressure drops in order to maintain the same total energy.