### Holland Tunnel Problem

 On Oct 29, 2012 Hurrcane Sandy Flooded the Holland Tunnel that passes Under the Hudson River! The Tunnel has two tubes: One is 8558 feet long And the other is 8371 feet long Both are 12.5 feet high by 20 feet wide! => (8558 + 8371)*20*12.5 = 4,232,250 Cubic Feet of Water Let's assume you want to pump this water out in 72 hours (or 3 days). If your pumps have six inch diameter pipes and can Pump at a pressure of 50 psi, How many pumps will you need to empty these Tunnels in 72 hours? The Volume of water for a 6 inch pipe at 50 psi Equals 9.5448*D*D*(Sq-Rt(P)) => 9.5448*(1/2)*(1/2)*(Sq-Rt(50)) => 16.872982 Cubic Feet per Second Where P = Pressure = psi And D = Pipe Diameter in feet = 1/2 foot Water Speed = V = Sq-Rt(2*g*h) Where g = 32 ft/s/s and h = feet depth => V = 8*(Sq-Rt(h)) since 2*g = 64 And Water Pressure k = 62.4/144 psi per foot depth => If P = 50 psi => Convert psi to Height of Water Column that results in 50 psi => (144/62.4)*50 = Height of Water Column to Create 50 psi => h = 115.38 Feet Area of Pipe = (((Pi)*D*D)/4) And V = 8*(Sq-Rt(h)) = Speed => (((Pi)*D*D)/4)*8*(Sq-Rt((144/62.4)*P) Equals the flow rate = Cubic-Feet per Second => 9.5448*D*D*(Sq-Rt(P)) Cubic-Feet per Second Enter-01: Enter Pipe Diameter D = 6 inches Enter-02: Enter Pump Ability Pressure P = 50 psi Enter-03: Enter Cubic Feet of Water = 4,232,250 Cubic-Feet to pump out Enter-04: Enter Pumping Hours = 72 hours = 3 days Result-01: b1 = y1/12 Convert D to Feet Result-02: b2 = (Sq-Rt(144/62.4))*(Pi/4)*8 = 9.5448 Result-03: b3 = b1*b1 = Diameter Squared Result-04: b4 = Sq-Rt(y2) ** (y2 = P = Pressure) Result-05: b5 = Cubic-Feet per Second of Pump Result-06: b6 = Cubic-Feet per Minute of Pump Result-07: b7 = Cubic-Feet per Hour of Pump Result-08: b8 = Gallons per Hour of Pump Result-09: b17 = Gallons per Second of Pump Result-10: b18 = Gallons per Minute of Pump Result-11: b19 = Gallons per Hour of Pump Result-12: b20 = Cubic Feet per Second of Pump Now to Calculate the Cubic-Feet per Second Needed to Pump out the Tunnel in 72 hours! Result-13: b9 = 4,232,250/72 Cubic-Feet per Hour Needed Result-14: b10 = b9/3600 = Cubic-Feet per Second Needed Surprise - Surprise You only need ONE Pump! Typical Fire Truck Pumps 1000 Gallons/Minute => 2.228 Cubic-Feet per Second If Fire Trucks are used: => 16.328125/2.228 = 7.3286 Fire Trucks => You would need 8 Fire Trucks to Pump the Tunnel in 72 Hours
 Water emerges from a fire hose at 64 ft/sec. If the rate of the flow is 180 gallons/minute, find the horse power of the pump motor if the efficiency of the pump is 50%. Also, find the force to hold the fire hose. Enter-01: Enter V = 64 ft/sec Enter-02: Enter Flow = 180 Gallons/Minute Enter-03: Enter-04: Enter-05: Result-01: => b1 = 180/7.48 = cubic-ft/min = 24.06417 Result-02: => b2 = (180/7.48)/60 = cubic-ft/sec = .4010695 Result-03: => b3 = (180*62.4)/(7.48*60) Lbs/sec = 25.067 Result-04: => b4 = b3*64 = 1601.711 ft-lbs/sec Result-05: => b5 = b4/550 = 2.9122 Horse Power Result-06: => b6 = b5*2 = Horse Power at 50% efficiency Result-07: => b7 = (b6*550)/64 = Lbs Force F = (550*HP)/V 