Answer:
The diameter at the bottom of the sprue is =0.725 in, and the sprue will not occur when 0.021<0.447.
Explanation:
Solution
The first step to take is to define the Bernoulli's eqaution
h effective = v²top/2g + ptop /ρg = hbottom + v² bottom/2g + p bottom/ ρg
h effective + 0 +0= 0 +v² bottom/2g + 0
Thus,
v bottom = √ 2gh total
=√ 2 (32. 6 ft/ s²) + (12/12 ft)
Which is = 8.074 ft/s
We now, express the relation for flow rate.
Q =π/4 D² bottom v bottom
= 40 in 3/s = π/4 D²₃ ( 8.074 ft/s) (12 in/ ft)
so,
D bottom = 0.725 in.
Then,
We express the relation to avoid aspiration
A₃/A₂ < √ h top /h total
= π/4 D²₃/ π/4 D²₂ < √3/15
= 0.725²/5² < √3/15
=0.021<0.447
Therefore, the aspiration will not happen or occur
