Pressure at Depth in a Liquid

What you’ll learn

Separate pressure due to liquid depth from total pressure.

បែងចែកសម្ពាធដោយជម្រៅអង្គធាតុរាវពីសម្ពាធសរុប។

Meaning and use

In a stationary liquid of approximately constant density, pressure increases with vertical depth. The increase rho gh is gauge pressure relative to the liquid surface. Total pressure includes the surface pressure, often atmospheric pressure for an open container. Depth is vertical, not distance along a sloping container wall.

ក្នុងអង្គធាតុរាវស្ងៀមមានម៉ាសមាឌប្រហែលថេរ សម្ពាធកើនតាមជម្រៅបញ្ឈរ។ ρgh ជាសម្ពាធបន្ថែមពីផ្ទៃ។ សម្ពាធសរុបត្រូវបូកសម្ពាធលើផ្ទៃ។

Formulas

Pressure increase below the surface

\[\Delta p=\rho gh\]

Total pressure

\[p_{\mathrm{total}}=p_{\mathrm{surface}}+\rho gh\]

Symbols and units

Symbol	Meaning	Unit or restriction
ρ	Liquid density	kg/m³
g	Gravitational field strength	N/kg
h	Vertical depth below surface	m
p, Δp	Pressure or pressure increase	Pa

Conditions and limits

• Assume the liquid is stationary and density is approximately constant.
• Examples use g = 10 N/kg; water density is taken as 1000 kg/m³.
• កុំច្រឡំសម្ពាធបន្ថែម និងសម្ពាធដាច់ខាត។

Worked examples

Water at depth

Find the pressure increase at 2 m depth in water.

1. Use \(\Delta p=\rho gh\).
2. Calculate \(1000\times10\times2=20000\) Pa.

20000 Pa gauge pressure

នេះជាសម្ពាធបន្ថែមពីជម្រៅ មិនទាន់រួមសម្ពាធបរិយាកាស។

Including surface pressure

Surface pressure is 100000 Pa; depth is 3 m in water.

1. Liquid contribution \(1000\times10\times3=30000\) Pa.
2. Total \(100000+30000=130000\) Pa.

130000 Pa total pressure

ត្រូវបូកសម្ពាធលើផ្ទៃបើសួរសម្ពាធសរុប។

Common mistakes

Instead of	Use	Why
ρgh always gives total absolute pressure.	It gives the increase below the surface.	Add surface pressure for the total.
Use distance along the container wall as h.	Use vertical depth.	Gravity acts vertically in this model.

Practice

Solve these before revealing the worked solutions. Include units where relevant.

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Water depth 0.5 m, ρ = 1000 kg/m³, g = 10 N/kg: find pressure increase.
2. Oil density 800 kg/m³ at depth 2 m, g = 10 N/kg: find increase.
3. At the same depth in the same stationary liquid, does a wider container alone increase pressure?

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 5000 Pa

   1000 × 10 × 0.5 = 5000.

2. 16000 Pa

   800 × 10 × 2 = 16000.

3. No.

   The model depends on density, g, and depth, not container width.

Quick recap

• Use vertical depth.
• Distinguish gauge increase from total pressure.
• State density and g assumptions.