Air at a pressure of 1 bar and 23(deg)C moves through 200 m of a 3 cm diameter smooth coil of tubing in Johns Hopkins Hospital's cardiovascular unit at a rate of 10 m^3/s. Calculate the pressure drop in the line.
Work:
p1 = 1 bar, Q = flow rate = 10 m^3/s, L = length of tubing = 200 m,
T = 23(deg)C, d = diameter of tubing = 3 cm = 0.03 m, sw = specific weight
g = gravitational constant, V = volume, Rd = Reynolds number
h = (p2 - p1)/sw
(p2 - p1) = [(f*L/d*V^2/2g)*sw]
f = 64/Rd and V = Q/A
Rd = (4*ro*Q)/(pi*d*mu)
(p2 - p1) = (f*L/d*V^2/2g)*sw
[(64*pi*d*mu/4*ro*Q)*(L/d)*(V^2/2g)]*sw
(p2 - p1) = [(16*pi*0.03 m*mu/10 m^3/s)*(200 m/0.03 m)*(V^2/19.6 m/s^2)]*sw
V = (10 m^3/s)*[200 m*pi*(0.015 m)^2] = 1.4 m/s
V^2 = 1.99 m^2/s^2
(p2 - P1) = (102.6*mu)*sw
(p2 - p1) = (f*L/d*V^2/2g)*sw
(p2 - p1) = (102.6*mu)*sw