A fountain with an opening of radius 0.015m shoots a stream of water vertically

Question

A fountain with an opening of radius 0.015m shoots a stream of water vertically from ground level at 6.0m/s. The Density of water is 1000kg/m3.

a. Calculate the volume rate of flow of water.

b. The fountain is fed by a pipe that at one point has a radius of 0.025m and is 2.5m below the fountain's opening. Calculate the absolute pressure in the pipe at this point.

c. The fountain owner wants to launch the water 4.0m into the air with the same volume flow rate. A nozzle can be attached to change the size of the opening. Calculate the radius needed on this new nozzle.

Explanation / Answer

a)calculate thevolume rate of flow of water .

     {Volume Flow Rate} = F =
          = v*A
          = (6.0)*(Pi*(0.015)^2)
          = 0.004241 m^3/sec

b) the fountainis fed by a pipe that at one point has a radius of 0.025m and is2.5m below the fountain's opening. Calculate the absolute pressurein the pipe at this point.

     (v_pipe)*(A_pipe) = (v_pipe)*(Pi*(0.025)^2) = F = 0.004241
   ---->    (v_pipe) = 2.16 m/sec
     (P_pipe) =
          = (101325) + (1/2)**v^2 - (1/2)**(v_pipe)^2 + *g*h -*g*(0)
         = (101325) + (1/2)*(1000)*(6.0)^2 - (1/2)*(1000)*(2.16)^2 +(1000)*(9.8)*(2.5)
          = 141492 Pa

c) thefountain owner wants to launch the water 4.0m into the air with thesame volume flow rate. A nozzle can be attached to change thesize of the opening. Calculate the radius needed on this newnozzle.
     (1/2)**v^2 = *g*h
     ---->    v = Sqrt[ 2*g*h ]
     ---->    v = Sqrt[ 2*(9.8)*(4.0) ]
     ---->    v = 8.85437 m/sec
     {Volume Flow Rate} = F = 0.004241 =
          = v*A
          = (8.85437)*(Pi*(R )^2)
     ---->    R = 0.0123 meter

Please, RATE! Thank you!

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