Question

A double nozzle lying in a horizontal x-y plane discharges water into the atmosphere at a rate of 0.5 m3 /s. Assume the water speed in jets A (10 cm in diameter) and B (12 cm in diameter) are the same. The pipe is 30 cm in diameter. Find the force acting on the flange bolts required to hold the nozzle in place.

Answer 1

Answer:

46.25KN

Explanation:

It is shown in the picture attached

Answer 2

Answer:

The force is  $F= 46.25kN$

Explanation:

The diagram for this question is shown on the first uploaded image  

At Equilibrium the summation of the of force on the vertical axis is zero

         i.e   $\sum F_y =0$

=>            $F_y sin \ 60^o =\rho Q (v_2 -v_1 cos \ 30^o)$

 $v_2$ is the is the speed of water at the nozzle which can be mathematically evaluated as

                      $v_2 = \frac{R}{A_n}$

substituting  $0.5m^3/s$ for R and $\frac{\pi}{4}(12*\frac{1m}{100} )^2$ for $A_n$

                    $v_2 = \frac{0.5}{\frac{\pi}{4} * (12*\frac{1}{100} )^2 }$

                         $= 44.23 m/s$

 $v_1$ is the is the speed of water at the pipe which can be mathematically evaluated as

                       $v_1 = \frac{R}{A_p}$

substituting  $0.5m^3/s$ for R and $\frac{\pi}{4}(30*\frac{1m}{100} )^2$ for $A_p$

                                $v_1 = \frac{0.5}{\frac{\pi}{4} * (30*\frac{1}{100} )^2 }$

                                    $= 7.07 m/s$

$\rho$ is he density of water with value $\rho =1000 kg /m^3$

Substituting values into the equation above

                  $F_ysin 60^o = 1000 (0.5) (44.23 -7.07 cos 30)$

                                 $= 21.99kN$

At Equilibrium the summation of the of force on the horizontal axis is zero

                  i.e   $\sum F_x =0$

=>            $F_y sin \ 30^o =\rho Q (v_2 -v_1 sin \ 30^o)$

               Since The speed at both A and B nozzle are the same then $v_2$ remains the same

 Substituting values

               $F_x sin30^o =1000 (0.5) (44.23 - 7.07*sin30)$

=>                        $F_x = 40.69kN$

   Hence the force acting on the flange bolts required to hold the nozzle in place is

                      $F = \sqrt{F_x^2 + F_y^2}$

                         $= \sqrt{40.69 ^2 + 21.99^2}$

                         $F= 46.25kN$