summer project ahood2
TRANSCRIPT
Summer Project
Fluid Mechanics
Dr. Thrash
Antoine Hood
2581660
Problem # 5
July 16, 2016
Known Information
1. Top of tank is open to atmosphere therefore pressure is zero at top of tank
2. Power of pump = 500 Watts3. Height = 2 meters4. Material is Cast Iron Roughness = 0.260mm =
0.00026m5. Total length of pipe = 7 meters6. Diameter = 50mm = 0.050 m7. Water temperature = 20 Celsius therefore Viscosity = 1.01
x 10^-3 (N x S)/(m^2)8. Standard elbow 90 degrees (L/D) = 30
More guess and check!!
Guess Re = 400,000
Re = (pVD)/(u)
400,000 = 49,505V
V = 8.08 m/s
Find Friction factor from Moody Chart knowing that relative roughness = 0.0052
Therefore friction factor = 0.032
Now solveDeltaHpump = 29.43(m^2)/(s^2) + 32.6(m^2/s^2) X 6.44)
DeltaHpump = 239.37(m^2/s^2)
DeltaP = DeltaHPUMP x row
DeltaP = 239,374 Pa
W = Q X DeltaP
Q = W/DeltaP
Q = .00209 (m^3/s)
Last Guess and check
RE = 40,000
Re = (pVD)/(u)
60,000 = 49,505V
V = 1.21 m/s
Find Friction factor from Moody Chart knowing that relative roughness = 0.0052
Therefore friction factor = 0.040
Now solveDeltaHpump = 29.43(m^2)/(s^2) + 0.7321(m^2/s^2) X (7.80)
DeltaHpump = 35.14(m^2/s^2)
DeltaP = DeltaHPUMP x row
DeltaP = 35,140 Pa
W = Q X DeltaP
Q = W/DeltaP
Q = .01423 (m^3/s)
Program Code
Reo = input('enter guess for the reynolds number ');mu = 0.00101;rho = 1000;D1=0.050;A1 = pi*(D1^2)/4;rr1=0.26/50%calculate V, Q, friction factor and head loss for section 1Vo = Reo*mu/(rho*D1);Qo = Vo*A1;fo = 1/(-1.8*log10(((rr1/3.7)^1.11 + 6.9/Reo)))^2;ho = [fo*(17/D1)*(Vo^2)/2]+ [fo*30*(Vo^2)/2]+[0.99875*(Vo^2)/2];%Root energy blalnce equation Hpump = 29.43 + ((Vo^2)/2)*(140*fo +30*fo +0.99875);Pressuredrop = Hpump * 1000Q1= 500/Pressuredrop% Display resultsx = [Reo ];y = [ho ];z = [Qo];t = [Q1]ff1 = [fo ];disp(' Reo')disp (x)disp(' ho ')disp(y)disp(' Qo ')disp(z)disp(' fo ')disp ('Q1 ')disp(t)disp(ff1)
Sample iterations
Iteration1
Re = 500,000
Relative roughness = .0052
Pressure drop = 32,750 Pa
Q1 = 0.0014 using power given
Qo = .0020 m^3/s using Q = VA
Headloss = 6.63 m^2/s^2
Friction factor = 0.0324
Iteration 2
Re = 50,000
Relative roughness = .0052
Pressure drop = 32,750 Pa
Q1 = 0.0153 m^3/s using power given
Qo = .0020 m^3/s using Q = VA
Headloss = 6.63 m^2/s^2
Friction factor = 0.0324
Iteration 3
Re = 800,000
Relative roughness = .0052
Pressure drop = 8.46 x 10^5 Pa
Q1 = 5.91 x 10^-4 m^3/s using power given
Qo = .0317 m^3/s using Q = VA
Headloss = 1,623 m^2/s^2
Friction factor = 0.0309
Iteration 4
Re = 1,000,000
Relative roughness = .0052
Pressure drop = 1.30 x 10^6 Pa
Q1 = 3.83 x 10^-4 m^3/s using power given
Qo = .0317 m^3/s using Q = VA
Headloss = 2,534 m^2/s^2
Friction factor = 0.0309
Iteration 5
Re = 20,000
Relative roughness = .0052
Pressure drop = 2.99 x 10^4 Pa
Q1 = 0.0167 m^3/s using power given
Qo = .0317 m^3/s using Q = VA
Headloss = 1.1252 m^2/s^2
Friction factor = 0.0346
Table of values
i Re f Q1 Pdrop HL
1 20000 0.0346 0.0167 29900 1.1252
2 50000 0.0324 0.0153 32750 6.63
3 500000 0.0324 0.0014 498000 600
4 800000 0.0309 .000591 846000 1623
5 1000000 0.0309 0.000383 1300000 2534
