1. (a) A 60 cm high, 40 cm diameter cylindrical water tank is being transported on a level road. The highest acceleration anticipated is 4 m/s2. Determine the allowable initial water height in the tank if no water is to spill out during acceleration. (b) Suppose the cylinder of part (a) is completely filled up to 60 cm, and then sealed with a lid. At the maximum acceleration of 4 m2/s, the minimum pressure in the containeris 100 kPa. What is the value and location of the maximum pressure

a) y = 0.522 m = 52.2 cm

b) Pmax = 105886 Pa = 105.89 kPa

Explanation:

H = 60 cm = 0.60 m

D = 40 cm = 0.40 m

a = 4 m/s²

ay = g = 9.81 m/s²

a) h = ?

If we apply

tan ∅ = ax/ay = (4 m/s²) / (9.81 m/s²) = 0.4077

⇒ ∅ = tan⁻¹ (0.4077) = 22°.18

then

tan ∅ = Δy / (D/2) ⇒ Δy = D*tan ∅/2

⇒ Δy = 0.40 m*tan (22°.18) / 2

⇒ Δy = 0.077 m = 7.7 cm

Thus, the allowable initial water height in the tank if no water is to spill out during acceleration is

y = H - Δy = 0.60 m - 0.077 m = 0.522 m = 52.2 cm

b) If Pmin = 100 kPa = 10⁵ Pa

we use the formula

Pmax = Pmin + ρ*g*H = (10⁵ Pa) + (1000 Kg/m³) * (9.81 m/s²) * (0.60 m)

⇒ Pmax = 105886 Pa = 105.89 kPa