Answer:
a) y = 0.35 m, b) hydrostatic balance
Explanation:
a) For this fluid mechanics exercise, let's use that the pressure at a given level is the same, let's set a level on the bell shape.
The pressure inside is
P_interior = P₀ + ρ g h ’
The pressure outside
P_exterior = Pₐ + ρ g h
as the point is at the same level the pressures are equal
P_interior = P_exterior
P₀ + ρ g h ’= Pₐ + ρ g h
h ’= (Pₐ- P₀) + ρ g h
To calculate P₀ they indicate that the pressure increases 10⁵ Pa for every 10 m, we use a direct rule of proportions or rule of three
P₀ = 10⁵ (40 + h ’) / 10 = 4 10⁵ + h’ 10⁴
the positive sign is because the water inside the hood also increases the air pressure.
we substitute
(4 10⁵ + h’ 10⁴) + ρ g h’ = Pₐ + ρ g h
h’ (ρ g + 10⁴) = Pₐ - 4 10⁵ + ρ h h
h’ (1000 9.8 + 10⁴) = (1 10⁵ -4 10⁵) + 1000 9.8 40
h' (1.98 10⁴) = -3 105 + 3.92 10⁵
h’ =
h ’= -4.65 m
as the hood is only 5 m high, the free air space is
Y = 5 - 4.65
y = 0.35 m
it is very little free space
B) The pressure outside and inside the hood is the same, the water rises inside the hood until the pressures equalize and at this point the force is equal and in the opposite direction, which is why the system is in hydrostatic balance.