File:C:\Users\Fidel\OneDrive\Documentos\EES\201608_Fidel_V_Examen1.EES 14/12/2016 13:40:47 Page 1 EES Ver. 10.104: #3961: For use only by students and instructors at Instituto de Ingeniera, UNAM, MEXICO
"A town engineer has been asked to determine the size of a water main needed to supply a new residential development. The main will be supplied from a tank whos minimum water level is 200ft above the grade level in the development. The lenght L of the main will be 3 miles. To provide fire protection, a flow of 10 000 gallons per minut at no less than atmospheric pressure in the main must be available at the development site. Availabe pipe sizes are 12 in, 18 in, 24 in, 36in and 48 in inside diameter D, with a roughness height E= 0.01in. a) if a 12 in diameter pipe were used, calculate the loss in head Delta h_f between the supply tank and the development site. b) What is the mininmum size of pipe that should be used? c) What will be the main pressure at the development site for this pipe size when carrying the requierd flow?" "Datos" DELTAZ = 200 [ft]*convert(ft;m) L=3[miles]*convert(miles;m) Q_0=10000[gallons/minute]*convert(gallons/minute;m^3/s) epsilon=0,01[in]*convert(in;m) D_1=12[in]*convert(in;m) D_2=18[in]*convert(in;m) D_3=24[in]*convert(in;m) D_4=36[in]*convert(in;m) D_5=48[in]*convert(in;m) rho_agua=1000[kg/m^3] mu_agua=viscosity(Water;v=(1/rho_agua);P=1[atm]*convert(atm;kPa)) g=9,81[m/s^2] gamma=rho_agua*g h_min=200[ft]*convert(ft;m) "(a)" A_1=pi*(D_1/2)^2 V_1=Q_0/A_1 Re_a=(rho_agua*V_1*D_1)/(mu_agua) RR_a=epsilon/D_1 f_a=moodychart(Re_a; RR_a) R_1=(8*f_a*L)/(g*(pi^2)*(D_1^5)) DELTAh_f_a=R_1*(Q_0^2) "(b)" {D_in=D*convert(m;in) P_1_min=(gamma*h_min)*convert(Pa;KPa) A=pi*(D/2)^2 V=Q_0/A Re=(rho_agua*V*D)/(mu_agua) RR=epsilon/D f=moodychart(Re; RR) R=(8*f*L)/(g*(pi^2)*(D^5)) DELTAh_f=R*(Q_0^2) P_2=P_1_min-((DELTAh_f*gamma))*convert(Pa;KPa) } "(c)" D_c=24[in]*convert(in;m) D_in_c=D_c*convert(m;in) P_1_min=(gamma*h_min)*convert(Pa;KPa) A_c=pi*(D_c/2)^2 V_c=Q_0/A_c Re_c=(rho_agua*V_c*D_c)/(mu_agua) RR_c=epsilon/D_c f_c=moodychart(Re_c; RR_c) R_c=(8*f_c*L)/(g*(pi^2)*(D_c^5)) DELTAh_f_c=R_c*(Q_0^2) P_2_c=P_1_min-((DELTAh_f_c*gamma))*convert(Pa;KPa)
A town engineer has been asked to determine the size of a water main needed to supply a new residential development. The main will be supplied from a tank whos minimum water level is 200ft above the grade level in the development. The
File:C:\Users\Fidel\OneDrive\Documentos\EES\201608_Fidel_V_Examen1.EES 14/12/2016 13:40:47 Page 2 EES Ver. 10.104: #3961: For use only by students and instructors at Instituto de Ingeniera, UNAM, MEXICO
lenght L of the main will be 3 miles. To provide fire protection, a flow of 10 000 gallons per minut at no less than atmospheric pressure in the main must be available at the development site. Availabe pipe sizes are 12 in, 18 in, 24 in, 36in and 48 in inside diameter D, with a roughness height E= 0.01in. a) if a 12 in diameter pipe were used, calculate the loss in head Delta hf between the supply tank and the development site. b) What is the mininmum size of pipe that should be used? c) What will be the main pressure at the development site for this pipe size when carrying the requierd flow?
Datos DZ
= 200
L = 3
[ft] ·
[miles] ·
m ft
0,3048 ·
m miles
1609,344 ·
Q 0 = 10000 [gallons/minute] ·
e = 0,01
[in] ·
0,0254 ·
m in
D 1 = 12
[in] ·
0,0254 ·
m in
D 2 = 18
[in] ·
0,0254 ·
m in
D 3 = 24
[in] ·
0,0254 ·
m in
D 4 = 36
[in] ·
0,0254 ·
m in
D 5 = 48
[in] ·
0,0254 ·
m in
= 1000
m agua
= Visc water ; v =
1 r agua
g = 9,81 [m/s2] g = r agua · g = 200 [ft] ·
(a)
A1 = p ·
V1 =
Q0 A1
D1 2
m3/s gallons/minute
;P= 1
101,325 ·
[kg/m3]
r agua
h min
0,0000630902 ·
2
0,3048 ·
m ft
[atm] ·
kPa atm
File:C:\Users\Fidel\OneDrive\Documentos\EES\201608_Fidel_V_Examen1.EES 14/12/2016 13:40:47 Page 3 EES Ver. 10.104: #3961: For use only by students and instructors at Instituto de Ingeniera, UNAM, MEXICO r agua · V 1 · D 1
Re a =
m agua
RR a =
e D1
f a = MoodyChart Re a ; RR a R1 =
Dh f;a
8 · fa · L g · p
2
· D1
= R1 · Q0
5
2
(b) (c)
D c = 24
[in] ·
D in;c = D c ·
P 1;min
Re c =
RR c =
39,37 ·
= g · h min ·
Ac = p ·
Vc =
0,0254 ·
Dc 2
m in
in m 0,001 ·
kPa Pa
2
Q0 Ac r agua · V c · D c m agua e Dc
f c = MoodyChart Re c ; RR c Rc =
Dh f;c
8 · fc · L g · p
2
· Dc
= Rc · Q0
5
2
P 2;c = P 1;min – Dh f;c
· g ·
0,001 ·
SOLUTION Unit Settings: SI C kPa kJ mass deg A1 = 0,07297 [m2] Dhf,a = 1149 [m] DZ = 60,96 [m] D2 = 0,4572 [m]
kPa Pa
Ac = 0,2919 [m2] Dhf,c = 31,61 [m] D1 = 0,3048 [m] D3 = 0,6096 [m]
File:C:\Users\Fidel\OneDrive\Documentos\EES\201608_Fidel_V_Examen1.EES 14/12/2016 13:40:47 Page 4 EES Ver. 10.104: #3961: For use only by students and instructors at Instituto de Ingeniera, UNAM, MEXICO
D4 = 0,9144 [m] Dc = 0,6096 [m] e = 0,000254 [m] fc = 0,01676 2 2 g = 9810 [kg/m -s ] L = 4828 [m] P1,min = 598 [KPa] Q0 = 0,6309 [m3/s] Rec = 914788 RRa = 0,0008333 R1 = 2888 [s2/m5] V1 = 8,647 [m/s]
D5 = 1,219 [m] Din,c = 24 [in] fa = 0,01904 g = 9,81 [m/s2] hmin = 60,96 [m] magua = 0,00144 [kg/m-s] P2,c = 288 [KPa] Rea = 1,830E+06 3 ragua = 1000 [kg/m ] RRc = 0,0004167 Rc = 79,41 [s2/m5] Vc = 2,162 [m/s]
No unit problems were detected.
Parametric Table: D vs P_2
P2 [KPa]
Run 1 Run 2 Run 3 Run 4 Run 5
Din
D
P2
[in]
[m]
[KPa]
12 18 24 36 48
0,3048 0,4572 0,6096 0,9144 1,219
-10678 -772 288 559,1 588,9
1000 900 800 700 600 500 400 300 200 100 0 -100 -200 -300 -400 -500 -600 -700 -800 -900 -1000 10
48[in]
36[in]
24[in]
18[in]
20
30
Din [in]
40
50
