# Evan's Space

## Wonders of Physics ## N2004 P1 Q15 – Pressure P1V1 = P2V2

Water if depth 10 m exerts a pressure equal to atmospheric pressure. An air bubble rises to the surface of a lake which is 20 m deep. When the bubble reaches the surface, its volume is 6 cm3.

What was the volume of the air bubble at the bottom of the lake?

A) 2 cm3          B) 3 cm3         C) 12 cm3      D) 18 cm3

Solutions: Option A
Since the air bubble is enclosed, PV at A is equal to PV at B.

PAVA = PBVB

(Patm + Pwater) VA = (Patm) VB

(10 + 20) VA = 10 x 6

VA = 60 / 30

= 2 cm3

## Using barometer to estimate height of mountain

At sea-level, the barometer which Pie is holding reads 760 mm of Hg. When he is at the top of Mount Pie, the same barometer reads 230 mm of Hg.
Given take the density of mercury to be 13.6 g cm-3 and the density of air, 1.23 x 10-3 g cm-3.

Estimate the height of the mountain? Solutions: 5860 m

Pressure difference in mercury, Pmercury = pgh

= 13600 x 10 x (0.76 – 0.23)

= 72080 Pa

Pressure difference, Pair = pgh

72080 = 1.23 x 10 x h

h  = 5860 m

In general, barometer can be used to measure altitude as height increases, height of mercury column will decreases. Of course same calibration has to be done.  It is not practical to bring around a mercury barometer as its liquid, heavy and poisonous etc.

An aneroid barometer (no mercury inside though) is used to measure altitude more accurately.

## Pressure – Manometer and how mercury levels in both limbs move as pressure changes The diagram shows a manometer connected to a gas cylinder of large volume. The atmospheric pressure is 76 cm Hg.

Due to the pressure of the gas cylinder, the mercury level in the left limb is at 30 cm while the mercury level in the right limb is at 0 cm.

Actually there is a short-cut. If atmospheric pressure remains constant, when the pressure of the gas cylinder decreases by 20 cm Hg, the difference in mercury levels between the left and right limbs decreases from 30 cm Hg to 10 cm Hg.

If you understand this, straight away you will be able to tell that the mercury height difference between left limb and right limb is 10 cm Hg.

You can then consider the markings on the manometer.  When the drop in pressure is 20 cm Hg, note that mercury level on one limb will increase by 10 cm and the other limb will decrease by 10 cm. Shared equally!

## Liquid Pressure Video

Liquid pressure, P = ρgh.

ρ is the density of the liquid (kg/m3) ,
g is t
he gravitational field strength (10 N/kg), and
h is the vertical height from the surface of the liquid (m)

In this video, since the last outlet is the lowest (greatest height from the liquid surface), the pressure is the greatest. Hence water ejects out with the greatest force and longest distance.

<p><a href=”https://vimeo.com/24961365″>Liquid Pressure</a> from <a href=”https://vimeo.com/user7367248″>evantoh</a&gt; on <a href=”https://vimeo.com”>Vimeo</a&gt;.</p>

## Hydraulic System – Basic Concepts

Hydraulic System is a useful system which allows you to lift heavy load by just applying a small force.

Liquid is used (over gas) in hydraulic system as liquid is incompressible.

Enclosed liquid is able to transmit pressure to all parts of the system. In other words, pressure throughout the system is constant.

View the video tutorial for the concept of hydraulic system and Conservation of Energy.