(i) Pressure decreases as one ascends the atmosphere If the density of air is p, what is the Change - Physics - Mechanical Properties Of Fluids

Question

(i) Pressure decreases as one ascends the atmosphere If the density
of air is p, what is the Change in pressure dp over a differential
height dh?
(ii) Considering the pressure p to be proportional to the density,
find the pressure p at a height h if the pressure On the surface of
the earth is p o
(iii) If p o = 1 03 x 10 3 N m 2 , p o =1 29 kg m - 3 , g = 9 8 m s
- 2 at what height will be pressure drop to 1 10 the value at
surface of the earth?
(iv) This model of the atmosphere works for relatively small
distances Identifying the underlying assumptions that limits the
model
(v) Explain in brief what will happen, if the length of the
capillary tube is smaller than the height to which the liquid
rises?

Pintu B. · Accepted Answer

Dear Student ,
The phenomenon of rise or fall of liquid in a capillary tube is called capillarity.

Consider a liquid whose angle of contact with the glass capillary tube is acute and so we have a concave surface as shown. Let ‘S’ be the surface tension of the liquid and ‘a’ is the radius of the capillary tube and ‘r’ is the radius of the concave surface of liquid. 'ρ' is the density of the liquid.

Pressure difference between two sides of top surface, P_a − P₀ = 2S/r

Considering points A and B, they must be at same pressure i.e.,

P₀ + hρg = P_a

Thus, height to which the liquid rises is

Regards

Pressure difference between two sides of top surface, Pa − P0 = 2S/r

Considering points A and B, they must be at same pressure i e , P0 + hρg = Pa

Thus, height to which the liquid rises is

Regards