Units (Solids, Liquids and Gases)
5 marks · NormalA cylindrical tube has an internal cross-sectional area of 0.003 m². The tube is filled with oil to a height of 1.2 m. The density of oil is 850 kg/m³. Take g = 10 N/kg.
Calculate the pressure difference between the top and bottom of the oil column.
Calculate the total force that the oil exerts on the base of the tube due to its pressure.
State how the pressure at the bottom changes if the height of the oil is doubled. Explain your answer.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) 10,200 Pa · must show Uses p = h × ρ × g
(b) 30.6 N · must show Uses F = p × A with previous answer
(c) The pressure at the bottom would double, because pressure in a liquid is directly proportional to height (p ∝ h). · must show States pressure increases linearly with height
Common mistakes: Using area instead of height for formula
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Substitutes correctly into p = h × ρ × g.
A1 (a) · 1 mark · Correct calculation and unit for pressure difference.
M2 (b) · 1 mark · Uses correct pressure from (a) and multiplies by area for force. (follow-through)
A2 (b) · 1 mark · Correct calculation of force, correct unit. (follow-through)
B1 (c) · 1 mark · States and explains that pressure is proportional to height, so doubling height doubles pressure.
Worked solution
a) p = h × ρ × g = 1.2 m × 850 kg/m³ × 10 N/kg = 10,200 Pa.
b) F = p × A = 10,200 Pa × 0.003 m² = 30.6 N.
c) If the height is doubled, the pressure difference at the bottom doubles. This is because pressure due to a liquid column increases in direct proportion to height (p ∝ h).