Question $3$

Water flows through a T$-$junction as shown in Figure $3.$ Assume that the $T$ is on a level plane $)=z_2=(z_3.$ The ball valve may be turned on or off but the velocity and pressure at $1$ remain the same at $u_1=2\frac{m}{s}$ and $p_1=10$kPa.

a$)$ When the valve is fully open, the flow velocity at $2$ is $1\mathrm{.}5\frac{m}{s}.$ Find the discharges in all three pipes;

b$)$ Apply Bernoulli equation and determine the pressure at $2.$

c$)$ With the ball valve fully closed and the flow velocity and pressure at $1$ remaining the same, determine the velocity and pressure at $3.$

d$)$ Following $($c$)$ above, determine the force required to hold the T$-$junction in position.

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