dP
dy
¼ Àqg
ðA2:20Þ
where q is the density of the fluid at height y. The Eq. (A2.20) is indicative of how
the hydrostatic pressure varies with the height within the fluid. The negative sign
indicates that the hydrostatic pressure decreases with increasing height in the fluid
or increases with increasing depth. This relation is valid for situations in which the
density varies with depth.
Integrating Eq. (A2.20) we will have:
Z P 2
P 1
dP ¼ À
Z y 1
y 1
qgdy ) P 2 À P 1 ¼ À
Z y 1
y 1
qgdy
ðA2:21Þ
Two particular cases for calculating the hydrostatic pressure variation are those
corresponding to liquids of uniform density and pressure variability in Earth’s
atmosphere. For liquids in which density variation can be neglect the integral of
Eq. (A1.22) will be:
P 2 À P 1 ¼ Àqgðy 2 À y 1 Þ
ð A2:22Þ
For the ordinary situation of a liquid in an open container, for example water in a
glass or a lake, there is an uncovered surface on top, making it necessary to measure
the depth of the liquid from that surface and to consider that the pressure on that
surface is the atmospheric pressure P o . So, we have for Eq. (A2.22), the following
expression:
P ¼ P o þ qgh
ðA2:23Þ
where the height h is equal to yy 2 – y 1 , P = P 1 and P 2 is replaced by P o . Figure A2.3 is
indicative of the stated principle that the pressure of a liquid (water) in a container is
independent of height, so its height will be equal in the four tubes of the left side
container, apart from the effects of capillarity (e.g., Asimov 1993). In the right-side
Fig. A2.3 Representative diagram of the pressure distribution of a liquid (e.g., water) in a container with multiple tubes on the left and two tubes separated by a porous membrane on the
right-side (adpt. Asimov 1993)
344
Annex A2: Basic Topics on Laws of Motion and Evaporation
dy
¼ Àqg
ðA2:20Þ
where q is the density of the fluid at height y. The Eq. (A2.20) is indicative of how
the hydrostatic pressure varies with the height within the fluid. The negative sign
indicates that the hydrostatic pressure decreases with increasing height in the fluid
or increases with increasing depth. This relation is valid for situations in which the
density varies with depth.
Integrating Eq. (A2.20) we will have:
Z P 2
P 1
dP ¼ À
Z y 1
y 1
qgdy ) P 2 À P 1 ¼ À
Z y 1
y 1
qgdy
ðA2:21Þ
Two particular cases for calculating the hydrostatic pressure variation are those
corresponding to liquids of uniform density and pressure variability in Earth’s
atmosphere. For liquids in which density variation can be neglect the integral of
Eq. (A1.22) will be:
P 2 À P 1 ¼ Àqgðy 2 À y 1 Þ
ð A2:22Þ
For the ordinary situation of a liquid in an open container, for example water in a
glass or a lake, there is an uncovered surface on top, making it necessary to measure
the depth of the liquid from that surface and to consider that the pressure on that
surface is the atmospheric pressure P o . So, we have for Eq. (A2.22), the following
expression:
P ¼ P o þ qgh
ðA2:23Þ
where the height h is equal to yy 2 – y 1 , P = P 1 and P 2 is replaced by P o . Figure A2.3 is
indicative of the stated principle that the pressure of a liquid (water) in a container is
independent of height, so its height will be equal in the four tubes of the left side
container, apart from the effects of capillarity (e.g., Asimov 1993). In the right-side
Fig. A2.3 Representative diagram of the pressure distribution of a liquid (e.g., water) in a container with multiple tubes on the left and two tubes separated by a porous membrane on the
right-side (adpt. Asimov 1993)
344
Annex A2: Basic Topics on Laws of Motion and Evaporation