Question

Water is flowing at 4.00m/s in a 12.00mm diameter pipe under a pressure of 2.000*10^4 N.m^2 in the basement is part of a closed system. What is pressure and speed of the water in a 7.00mm diameter pipe at the top of the 40.0m building? As clearly as possible please!

Answer 1

Bernouli's equation

   P + 1/2 * rho*v^2 + rho*g*h = constant

   P1 + 1/2 * rho*v1^2 + rho*g*h1 = P2 + 1/2 * rho*v2^2 + rho*g*h2

   from continuity equation A1V1 = A2V2
               ==> V2 = A1V1/A2
                       = pi*r1^2*v1/ PI*R2^2
                   = (6*10^-3)^2*4 / (3.5*10^-3)^2

       speed of water at top    = 11.755 m/s

now p2 is density of water rho = 1000 kg/m3, g = 9.8 m/s2, h1 = 0 m, h2 = 40 m,
   p1 = 2*10^4 N/m^2, v1 = 4m/s, v2 = 11.755 m/s

  
   P1 + 1/2 * rho*v1^2 + rho*g*h1 = P2 + 1/2 * rho*v2^2 + rho*g*h2

   P2 =(2*10^4) +(0.5*1000*4^2)+(1000*9.8*0 )- ((0.5*1000*11.755^2)+(1000*9.8*40))

   P2 = 433090.01 N/m^2