show your steps Data were obtained from measurement on horizontal section of iro
ID: 2993397 • Letter: S
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Data were obtained from measurement on horizontal section of iron pipe of 50 mm diameter. At one section the pressure was Pi=900 kpa. The pipe is 30 m long, the second section the pressure was P2=200 kpa. The volume flow rate of water was 0.015 m3/s. Estimate the relative surface roughness of the pipe. Consider the minor loses at the inlet (Kiniet=0-4) and the exit (Kext=0.6) of the pipe. Assume vh20 = 1.01 times 10-6, a1=a2=1 Let The drag force, F0, of an airfoil at zero angle of attack is a function of density, , viscosity, , velocity, V and length parameter, L. A 1/10 scale model of an airfoil was tested in a wind tunnel at a Reynolds number of 5.5 times 106. Test conditions in the wind tunnel air stream were 15degreeC and 10 bar. The prototype airfoil has a length of 2 m. and it is to be flown in air at standard atmospheric conditions (15 degree C. 101 kPa). Assume mu air= 1.79 times 10-5 Pa.s. Determine: A set of dimensionless groups suitable to characterize the model test results. The speed at which the model was tested. Vm. The corresponding prototype speed, Vp. Useful Relations Re = rho VL/mu = VL/vExplanation / Answer
1) P1 = 900 kPa
P2 = 200 kPa
z1 = z2 (generally pipes are horizontal)
Given Q = 0.015 m^3/s and D = 50mm = 0.05 m
Q = A*V and A = (pi/4)*D^2 = 1.96*10^-3
V = 0.015/1.96*10^-3 = 7.64 m/s
Since the pipe cross section is same
V1 = V2 = V = 7.64 m/s
H = (P1-P2)/rho*g + Kin*V^2/2*g - Kex*V^2/2*g
H = 700*10^3/(1000*10) + 7.64^2/20*(0.4-0.6)
H = 69.416
H = f*(L/D)*V^2/2*g
f*(30/0.05)*7.64^2 = 20*69.416
f = 0.0396
2)Given
Fd = fn(rho,mu,V,L)
Taking rho,V,L as Fundamental Variables and there are 2 Pi groups
Fd = kg m/s^2
rho = kg/m^3
V = m/s
L = m
mu = kg/m*s
Pi 1
Fd/rho*V^2*L^2
Pi 2
mu/rho*V*L = Re non dimensional no
From Re equation
(Re)p = (Re)m = 5.5*10^6
Given
Lp/Lm = 1/10
mu and Rho are constants
From Re equation
Vp*Lp = Vm*Lm
Vp/Vm = 10 ------(1)
(Re)p = 5.5*10^6
rho*Vp*Lp = mu*5.5*10^6
1000*Vp*2 = 1.79*10^-5*5.5*10^6
Vp = 0.05 m/s
Vm = 0.005 m/s
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