Liquid pressure

Содержание и основные понятия

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Alterna · physics · 3.2
Liquid pressure
Calculation of the pressure to be reported
At a depth of 10 metres, the water presses with force into the same atmosphere, and at the bottom of the Mariana falls there are 1,100 atmospheres. How can we calculate the pressure of the liquid?
GEF · Grade 7
PIF · Baseline
01
Calculation of the liquid pressure
The formula p = gh is the pressure on the bottom and the walls of the receptacle.
Liquid pressure formula
p = ρ · g · h
where:
is the density of the liquid (kg/m3)
g = 9.8 N/kg
h = depth (m)
It is important:
The pressure does not depend on the shape of the vessel and the area of the bottom — just the density of the liquid and the depth!
Example
Water pressure at 10 m depth: p = 1000 x 9.8 x 10 = 98000 Pa ER 98 kPa.
Each 10 m deep adds ~1 atmosphere of pressure.
🌊
Pressure at different depths
IV-025B · p = gh = depth visualization
Liquid:
Deep:
5
m
02
Communicating receptacles
Why is there water on the same level in the teapot and in the nose?
Communicating receptacles
Communicating receptacles
- these are vessels connected below the liquid level.
Law:
In reported receptacles, a uniform liquid is placed on the same level.
If the liquids are different:
ρ₁h₁ = ρ₂h₂
- heights are inversely proportional to density.
☕
Communicating receptacles
IV-025 · Liquid selection + single knee addition
Left liquid:
Right liquid:
Level:
100
%
C
What needs to be understood
Outcome 1
Explain the physical meaning of the topic "Vacuity pressure" through the model, not just through the formula.
Outcome 2
Explain and correctly use terms: hydrostatic pressure, reported receptacles, density.
Outcome 3
Indicate the conditions for the applicability of the law, verify units and limit cases.
T
Terms of the topic
The definition should indicate the physical meaning, not a substitute for a domestic synonym.
hydrostatic pressure
Pressure of the standing liquid due to its weight and external pressure on the surface.
Reported receptacles
Receptacles connected below the free surfaces in such a way that the liquid can flow between them.
density
The ratio of the mass of the homogeneous substance to the volume it holds.
depth
Distance downstream of the selected free surface to the point under consideration.
F
Origin and conclusion of the formulas
The fundamental law cannot be "proven" by algebras: for each record, it is stated whether it is a definition, an experimental law, or a model effect.
p
=
ρ
g
h
p=\rho gh
p
=
ρ
g
h
model effect
Pressure of the liquid column.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
V
=
S
h
,
m
=
ρ
S
h
V=Sh,\qquad m=\rho Sh
V
=
S
h
,
m
=
ρS
h
Above the S site, the vertical column of the standing liquid h height is removed and its mass is found.
F
=
m
g
=
ρ
S
h
g
F=mg=\rho Shg
F
=
m
g
=
ρS
h
g
The weight of the pole creates the force of pressure on the lower area.
p
=
F
S
=
ρ
g
h
p=\frac{F}{S}=\rho gh
p
=
S
F
​
=
ρ
g
h
The division of force by area removes dependence on the selected section of the pole.
Conditions:
A uniform, noncompressable liquid lies in a homogeneous field of gravity; p is the overpressure of the pole, the surface pressure is added separately.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
ρ
1
h
1
=
ρ
2
h
2
\rho_1h_1=\rho_2h_2
ρ
1
​
h
1
​
=
ρ
2
​
h
2
​
model effect
Equivalence of liquids.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
p
1
=
p
2
p_1=p_2
p
1
​
=
p
2
​
In the shared fluids, the pressure at one horizontal level at the border is equal.
p
1
=
ρ
1
g
h
1
,
p
2
=
ρ
2
g
h
2
p_1=\rho_1gh_1,\qquad p_2=\rho_2gh_2
p
1
​
=
ρ
1
​
g
h
1
​
,
p
2
​
=
ρ
2
​
g
h
2
​
Each pole creates hydrostatic pressure, determined by density and height.
ρ
1
g
h
1
=
ρ
2
g
h
2
⇒
ρ
1
h
1
=
ρ
2
h
2
\rho_1gh_1=\rho_2gh_2\Rightarrow\rho_1h_1=\rho_2h_2
ρ
1
​
g
h
1
​
=
ρ
2
​
g
h
2
​
⇒
ρ
1
​
h
1
​
=
ρ
2
​
h
2
​
The same g is reduced by linking the heights of the poles to the density of the liquids.
Conditions:
The non-mixable liquids lie in the communicating receptacles, the free surfaces are under the same pressure, g continuously.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
!
Model boundaries and typical errors
Error: Forget model condition
The key condition of this subject is that the density of the liquid (kg/m3) is the density.
How to Check the Mind
g = 9.8 N/kg Then check the units, vector orientation and result behaviour at zero or very large parameter.
Σ
Conclusion on the topic
Liquid pressure
At a depth of 10 metres, the water presses with force into the same atmosphere, and at the bottom of the Mariana falls there are 1,100 atmospheres. How can we calculate the pressure of the liquid?
is the density of the liquid (kg/m3)
g = 9.8 N/kg
Any numerical result shall be accompanied by a unit, a sign and an explanation of its physical meaning.
The content is consistent with the FRP on Physics of the OS/OSS 2025 and the subject matter of the current lines of the PNP: I. M. Peryškin and co-authors (7–9), G. J. Mäkishev and coauthors (10–11), and with the lines "Engineers of the Future" and V. A. Kasyanov. The original texts are not reproduced, the text of the textbooks is not reproduced.