IEMDaily - Video Lecture Notes

Definition

Measurement of Air Pressure

An instrument that measures air pressure is called a barometer.
The original instrument had mercury in the small basin, with an upside down glass tube placed in the mercury. As air pressure increased, the pressure would force more mercury in the tube. When pressure decreased, the level of mercury in the tube would go down.
This type of barometer is known as a mercurial barometer.
The height of mercury in the glass tube could be measured in inches. After measuring sea level air pressure many times, we now know that average sea level air pressure is 29.92 inches, this equals 76 centimeters.

Definition

Measurement of atmospheric pressure in terms of height of Mercury Column

If height of mercury column of the barometer or any tube raises by

h

then the amount of pressure change will be:

Δ p = h ρ g

Definition

Units of pressure

Some common units of atmospheric pressure are:
1. SI unit: Pascal (

P a

) or

N m^{- 2}

2. Atmosphere:

1 a t m = 1.013 \times 10^{5} P a

3. Bar:

1 b a r = 10^{5} P a

4. Torr:

1 t o r r = 133 P a

5. Millimeter of mercury:

1 m m H g = 133 P a

Law

Law of atmosphere

Law of atmosphere basically determines relationship between atmospheric pressure and height from the earth's surface.

According to this law:

P_{z} = P_{0} e^{\frac{- m g z}{k T}}

Where m is the molecular mass, g is the gravitational acceleration, k is Boltzmann's constant, and T is the temperature.

Definition

Standard Atmospheric Pressure

Standard Atmosphere is mainly used as a reference value for the average atmospheric pressure at sea level. 1 standard atmosphere is defined as being exactly equal to 101,325 pascals.
Since the atmospheric pressure varies with changes in weather and altitude, it is convenient to standardise on a single value so that ratings, measurements and specifications can be compared. In particular 1 Standard Atmosphere is used by the Aviation industry as the reference standard for sea level pressure.

Example

Experimental demonstration of atmospheric pressure

Fill a cup one-third with water. Cover the entire mouth with an index card. Holding the card in place, turn the cup upside down. Remove your hand from underneath.

Atmospheric pressure holds up the card and the water on it.

Definition

Siphon Tube

Siphon can be described as a tube or pipe that allows liquid to flow from the higher level to the lower level. Siphon allows liquids to flow uphill, above the surface of the tank or reservoir, without pumps. Liquids flow down the tube under the pull of gravity. The liquid is discharged at a level lower than the surface of the reservoir or the tank. The pull on the surface of liquids from a higher to lower altitude is known as siphoning. Records show that siphoning has been practiced in ancient cultures

Example

Problem on Siphon Mechanism

Example: A siphon has a uniform circular base of diameter

\frac{8}{\sqrt{π}}

with its crest

A

1.8 m

above water level as in figure. Then find velocity of flow, discharge rate of the flow and absolute pressure at the crest level.[Use

P_{0} = 10^{5} N / m^{2} g = 10 m / s^{2}

]

Solution:Applying the Bernoulli's equation, at top layer of water in water vessel and end of the pipe.

P_{D} + ρ g y_{D} + \frac{1}{2} ρ {v_{D}}^{2} = P_{C} + ρ g y_{C} + \frac{1}{2} ρ {v_{C}}^{2} Here P_{D} = P_{C} = P_{o} And v_{D} = 0 ∵ it is negligible and y_{D} - y_{C} = 3.6 m \Rightarrow P_{o} + ρ g (y_{D} - y_{C}) + 0 = P_{o} + \frac{1}{2} ρ {v_{C}}^{2} \Rightarrow v_{C} = \sqrt{2 g (y_{D} - y_{C})} = \sqrt{2 \times 10 \times 3.6} = 6 \sqrt{2} m/s

\Rightarrow

Discharge rate of water

= a v = π \times {(\frac{4}{\sqrt{π}})}^{2} \times 10^{- 4} \times 6 \sqrt{2} = 96 \sqrt{2} \times 10^{- 4} m^{3} / s

\Rightarrow

Now applying the Bernoull's theorem at point A and C, we have

P_{A} + ρ g y_{A} + \frac{1}{2} ρ {v_{A}}^{2} = P_{C} + ρ g y_{C} + \frac{1}{2} ρ {v_{C}}^{2} ∵ v_{A} = v_{C} and y_{A} - y_{C} = 1.8 + 3.6 = 5.4 m \Rightarrow P_{A} = P_{C} - ρ g (y_{A} - y_{C}) = 10^{5} - 1000 \times 10 \times 5.4 = 4.6 \times 10^{4} N / m^{2}

\Rightarrow

Result

Pressure variation with altitude

At a certain height above sea level, the weight of column of air above that height will be lesser than sea level. So pressure due to column of air decreases as height increases. This decrease is not linear but exponential. The pressure drops more rapidly initially and later the fall in pressure with height decreases.

Definition

Atmospheric pressure

Atmospheric pressure is the pressure caused by the weight of air above the earth's surface. Its value at sea level is