Question $2$

Liquid $(SG=1\mathrm{.}5)$ enters the "black sphere" through a $5cm$ pipe with a velocity of $10\frac{m}{s}$ and a pressure of $400$kPa. It leaves the sphere through two jets as shown in the figure below. The velocity in vertical jet is $30\frac{m}{s},$ and its diameter is $25mm.$ The other jet's diameter is also $25mm.$ Calculate the force $($Resultant and angle$)$ through $5cm$ pipe wall is required to hold the sphere in place. Assume the sphere $($plus the liquid inside$)$ has a weight of $600N.$ Sketch a diagram to show all the forces involved.

Hint: Both outflows are discharged to atmosphere.

Answer:

$F_R=\sqrt[\phantom{2}]{{36\mathrm{.}817}^2+{118\mathrm{.}983}^2}=124\mathrm{.}549N$