Evan's Space

Wonders of Physics


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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?mount_pie

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.

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Pressure – Manometer and how mercury levels in both limbs move as pressure changes

mount_pieThe 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!


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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>



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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.


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A common question on P=F/A but students always get confused.

Stool_1
Stool_2

Take note of all units. To find the pressure in Pa, the units for F must be N and the area must be m2.

For (a) and (b)

Note that pressure acting on the floor by all the 3 legs is the SAME as the pressure acting on the floor by each of the leg.

In this case, the total weight of Pie and the stool is spread over 4 legs.

F = weight = 65 x 10 = 650 N

A = 25 cm2 = 25 ÷ 1002 = 0.0025 m2

P = F/A = 650 / (0.0025 x 4) m2 = 65 000 Pa = 65 kPa

For (c)

When there are only 3 legs, the weight (still the same) is now spread over a smaller area. Hence pressure should increase.

P = F/A = 650 / (0.0025 x 3) m2 = 86666.67 Pa = 86 700 Pa = 86.7 kPa