Answer
$7.84\;cm/h$
Work Step by Step
Applying the Bernoulli’s equation between two points: one is the downspouts at height $h_1=11\;m$ and another is opening of floor drain at the height $h_2=1.2\;m$, we obtain
$p_1+\frac{1}{2}ρv_1^2+ρgh_1=p_2+\frac{1}{2}ρv_2^2+ρgh_2$
where, we take the level of the pipe $M$ as our reference level.
Here, the initial speed of the water in the downspout is negligible $v_1=0\;m/s$ and $p_1=p_2=p_{air}$
Therefore,
$ρgh_1=\frac{1}{2}ρv_2^2+ρgh_2$
or, $\frac{1}{2}ρv_2^2=ρg(h_1-h_2)$
or, $v_2=\sqrt {2g(h_1-h_2)}$
Substituting the given values
$v_2=\sqrt {2\times9.81\times(11-1.2)}\;m/s$
or, $v_2=13.87\;m/s$
The water from pipe M reach the height of the floor drain and threaten to flood
the basement.
By the continuity equation,
$A_2v_2=A_bv_b$
or, $v_b=\frac{A_2v_2}{A_b}$
or, $v_b=\frac{\pi\times 0.03^2\times 13.87}{30\times60}$
or, $v_b=2.178\times10^{-5}\;m/s$
or, $v_b=7.84\;cm/h$
Therefore, the rainfall rate is $7.84\;cm/h$
