Pressure in Solids and Liquids
Senior 2 · Physics
Pressure in Solids and Liquids
Lesson 3 of 5
20 min
Let's begin
Masons building a house in Rwanda often use a long clear hosepipe filled with water to mark points at exactly the same height on opposite walls. Water from a reservoir on a hilltop flows down through pipes to taps in the valley below. Both rely on one rule about connected containers of liquid.
Communicating vessels are containers joined at the bottom, so that one liquid can flow freely between them. When the liquid is at rest, it stands at the same level in every vessel, whatever their shapes or widths.
Why? Pressure depends only on depth (P = hρg). If the level were higher in one vessel, the pressure at the bottom of that vessel would be greater, and liquid would flow until the levels were equal.
Applications:
Non-miscible (immiscible) liquids do not mix: cooking oil and water, or paraffin and water. If you pour water into a U-tube and then add oil to one arm, the oil floats and pushes the water down on that side. The levels are no longer equal.
Measure both heights from the boundary (interface) between the two liquids. At that level, the pressures in the two arms are equal, so:
h₁ρ₁ = h₂ρ₂
The less dense liquid stands in the taller column.
Oil of density 800 kg/m³ is poured into one arm of a U-tube containing water (1000 kg/m³). The oil column above the interface is 10.0 cm. How high does the water stand above the interface in the other arm?
hw × 1000 = 10.0 × 800, so hw = 8.0 cm.
In a U-tube, 10.0 cm of an unknown oil balances 8.5 cm of water above the interface. Find the density of the oil.
ρoil = 1000 × 8.5 ÷ 10.0 = 850 kg/m³.
Tip
Measure from the interface, not from the bottom of the tube
Check your answer: the lighter liquid must have the TALLER column. If your answer gives the oil a shorter column than the water, you have inverted the ratio.
Three glass tubes of different shapes are joined at the bottom and filled with water. How do the water levels compare?
Solution: They are all the same, because the pressure at the bottom depends only on the depth of water, not on the shape.
Paraffin (800 kg/m³) is poured into a U-tube of water. The water column above the interface is 9.6 cm. How tall is the paraffin column?
Solution: h × 800 = 9.6 × 1000, so h = 12.0 cm.
Why must a kettle's spout reach as high as the top of the kettle?
Solution: The spout and the body are communicating vessels. Water in the body can only rise as high as the spout's opening before it pours out, so a short spout means the kettle cannot be filled.
Why is a water reservoir usually built on the highest hill in an area?
Solution: Water in connected pipes tries to reach the level of the reservoir, and the height difference gives pressure (hρg) that pushes water out of the taps in houses below, without pumps.
Summary
Sources and credits
The explanation of communicating vessels and non-miscible liquids, the Rwandan examples, the worked examples and the practice items are written by Ganzaa.
