Relation Between Bar and Atm: Units of Pressure

Ans.  Mass of girl (m) = 50 kg

Force on the heel (F) = mg = 50 9.8 = 490 N

Diameter of the heel (d) = 1.0 cm = 1 10^-2 m

Area (A) = π r d²/4 

= 3.14 (1 10^-2)² / 4 = 7.85 10^-5 m² 

Pressure (P) = F/A = 490 / 7.85 10^-5 = 6.24 10⁶ Pa

Ans. Pressure on the piston due to car = weight of car / Area of Piston

P = 3000 9.8 / 425 10^-4 Nm^-2 

= 6.92 10⁵ Pa

Ans. For water column in one arm of U tube, h₁ = 10.0 cm; ρ₁ (density) = 1 g cm^-3

For the spirit column in the other arm of the U tube, h₂ = 12.5 cm; ρ₂ =?

As the mercury columns in the two arms of the U tube are in level, therefore pressure

exerted by each is equal.

Hence h₁ρ₁g = h₂ρ₂g or ρ₂ = h₁ρ₁/h₂ = 10 x 1/12.5 = 0.8 g cm^-3

Therefore, relative density of spirit = ρ₂/ρ₁ = 0.8/1 = 0.8

Ans. Height of the water column, h₁ = 10 + 15 = 25 cm

Height of the spirit column, h₂ = 12.5 + 15 = 27.5 cm

Density of water, ρ₁ = 1 g cm^-3

Density of spirit, ρ₂ = 0.8 g cm^-3

Density of mercury = 13.6 g cm^-3

Let h be the difference between the levels of mercury in the two arms.

Pressure exerted by height h, of the mercury column = hρg

= h × 13.6g … (i)

Difference between the pressures exerted by water and spirit:

= ρ₁h₁g – ρ₂h₂g

= g(25 × 1 – 27.5 × 0.8)

= 3g … (ii)

Equating equations (i) and (ii), we get:

13.6 hg = 3g

h = 0.220588 ≈ 0.221 cm

Thus, the difference between the levels of mercury in the two arms is 0.221 cm.

Ans. Reynold’s Number is given by; 

NR = Dvc /  

where, 

= Density of liquid

D = Diameter of tube

vc = critical velocity

= coefficient of viscosity

If the value of NR lies between 0 to 2000, the flow of liquid will be streamlined and if its value lies above 3000, the flow of liquid will be turbulent. 

Ans. According to Poiseuille’s formula, the rate of flow of liquid through a tube of radius R

and length l is given by;

Q = R4 / 8l ……… (i)

If R and l are doubled, then the rate of flow will be 

Q’ = (2R)4 / 8(2l)

Q’ = 16R4 / 2(8l) ……… (ii)

Comparing eq. (i) and (ii)

Q’ = 8Q

Thus, the rate of flow of liquid will increase 8 times.

Ans. l = 1.5 m , r = 1 10^-2 m

Volume/s , V = (Mass/s) / Density 

= 4 10^-3 / 1.3 10³ m³ s^-1 = 4/1.3 10^-6 m³ s^-1 

= 0.83 Pa s

Now, V = pr4 / 8l (where, p is the pressure difference across the capillary)

p = 8Vl / r4 

p = 8 4/1.3 10^-6 0.83 1.5 7/22 1/10^-8 Pa

= 9.75 10² Pa

Reynold's number is 0.3. So, the flow is laminar. 

Ans. Water on a clean glass surface spreads because the force of cohesion of water is much less than the force of adhesion due to glass. In the case of mercury, the force of cohesion due to mercury is very strong as compared to adhesion force due to glass. As a result, mercury does not make the glass wet and tends to form drops. 

Ans. Law of floatation states that a body will float in a liquid, if weight of the liquid displaced by the immersed part of the body is at least equal to or greater than the weight of the body.

Ans. The height of the blood column in the human body is more at the feet than at the brain. We know that pressure is directly dependent on the height of the column. Thus, pressure is more at the feet than at the brain.

Ans. Surface tension is the tension caused at the surface caused by the attraction of particles in the surface layer by the bulk of the liquid, which tends to minimize surface area.

Ans. Archimedes’s Principle will not hold in a vessel in a freefall. This is because the acceleration due to gravity is zero and hence buoyant force will not exist.

Ans. Surface tension of water is much higher than in oil. Thus by adding oil to water, the water without oil pulls the oily water in the direction of the breeze, and sea waves calm down.

Ans. The cohesive forces between the oil molecules are less than the adhesive force between the oil molecules. The drop of oil spreads out and reverse holds for a drop of water. 

Ans. The terminal velocity is directly proportional to the square of the radius of the ball, therefore the ratio of terminal velocities will be 1:4.

Ans. Viscosity is the property of fluids by which the particles experience an internal friction that affects the flow of the fluid. This is why honey pours slowly than water.

Ans. Reynold’s number is given by,

\(\frac{SDV_c}{n}\)

Where,

S is density of liquid

D is diameter of tube

Vc is critical velocity

n is coefficient of viscosity

Ans. Bernoulli’s theorem is applied in atomizers and in the lift of an aeroplane wing.

Ans. In Bernoulli’s theorem, mass, energy and linear momentum are conserved.

Ans. No. Bernoulli"s equation cannot be used to describe the flow of water through a rapid in a river because of the turbulent flow of water. This principle can only be applied to streamlined flow.

Ans. As pressure column is high at the bottom, there is a high probability for cracks to be developed at the bottom. This is why dams are made thick at the bottom to counteract this pressure.

Ans. The atmospheric pressure is low at high altitudes. Due to greater pressure differences in blood pressure and atmospheric pressure, it is difficult to stop bleeding from a cut in the body.

Ans. [n] = M¹L^-2T^-2

[S] = M¹T²L⁰