Pressure: Question 3
Syllabus 1.8
A dairy processing plant stores fresh milk in a tall, cylindrical stainless-steel tank. Set into the curved side of the tank are two identical circular inspection hatches, each held shut by a ring of bolts: one hatch is near the top of the tank, and the other is near the base. When the tank is full of milk, maintenance engineers tighten far more bolts on the base hatch than on the top hatch to keep it sealed.
(a) State how the pressure due to the milk compares at the top hatch and at the base hatch when the tank is full. [1]
(b) Explain, in terms of the weight of milk above a point, why the pressure at the base hatch is greater than the pressure at the top hatch. [2]
(c) Explain, in terms of pressure and force, why the base hatch needs more bolts than the top hatch to stay sealed. [2]
(d) The plant considers replacing the milk with a cream product that is denser than milk, filled to the same maximum depth in the tank. State and explain how the pressure at the base hatch would compare with the pressure when the tank holds milk. [2]
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Worked solution
Part (a): Comparing pressure at the top hatch and the base hatch
The pressure due to the milk is greater at the base hatch than it is at the top hatch.
Part (b): Why pressure increases with depth
The base hatch sits much deeper below the surface of the milk than the top hatch does. Directly above the base hatch there is a tall column of milk, and this column has a much greater weight than the short column of milk above the top hatch. That greater weight presses down on the milk (and on the tank wall) at the base. Since pressure is force spread over area, a greater weight bearing down over the same hatch area means a greater pressure. This is why the pressure due to the milk increases with depth.
Part (c): Why the base hatch needs more bolts
Pressure produces a force by pushing outward on any surface it acts on. Both hatches have the same area, but because the pressure at the base hatch is greater, the outward force the milk exerts on the base hatch is also greater than the outward force on the top hatch. The bolts around each hatch have to supply an equal and opposite inward force to keep the hatch sealed against this push. Since the total outward force is much larger at the base, more bolts are needed there so that the load is shared between enough bolts to hold the hatch shut safely. Near the top, where the pressure, and so the outward force, is much smaller, fewer bolts are already sufficient.
Part (d): Comparing milk with a denser cream product
Pressure beneath the surface of a liquid depends on both the depth and the density of the liquid. At the same depth, the denser cream packs more mass into the same volume, so the column of cream above the base hatch has a greater weight than the equivalent column of milk would. A greater weight pressing down over the same hatch area gives a greater pressure. So if the tank held cream instead of milk, filled to the same maximum depth, the pressure at the base hatch would be greater than it is with milk.
Final answers
- (a) Pressure is greater at the base hatch than at the top hatch
- (b) A greater depth means a greater weight of milk above, giving a greater force per unit area (greater pressure)
- (c) The base hatch needs more bolts because the greater pressure there produces a greater outward force on the hatch, which more bolts are needed to resist
- (d) Denser cream at the same depth gives a greater pressure at the base hatch than milk does