Mechanical Properties of Fluids

Surface tension is exhibited by liquids due to the force of attraction between molecules of the liquid. The surface tension decreases with increase in temperature and vanishes at boiling point. Give that the latent heat of vaporisation for water Lv = 540 k cal/kg, the mechanical equivalent of heat J = 4.2 J/cal, density of water ρw = 103 kg/l, Avogadro’s number NA = 6.0 1026 k/mole, and the molecular weight of water MA = 18 kg for 1 k mole.

c) 1 g of water in the vapour state at 1 atm occupies 1601 cm3. Estimate the intermolecular distance at boiling point, in the vapour state. d) During vaporisation a molecule overcomes a force F,...

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surface tension is exhibited by liquids due to the force of attraction between molecules of the liquid. The surface tension decreases with increase in temperature and vanishes at boiling point. Give that the latent heat of vaporisation for water Lv = 540 k cal/kg, the mechanical equivalent of heat J = 4.2 J/cal, density of water ρw = 103 kg/l, Avogadro’s number NA = 6.0 1026 k/mole, and the molecular weight of water MA = 18 kg for 1 k mole.

a) Estimate the energy required for one molecule of water to evaporate. b) Show that the inter-molecular distance for water is Answer : a) According to the question, the latent heat of vaporization...

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c) If po = 1.03 × 105 N/m2, ρo = 1.29 kg/m3 and g is 9.8 m/s2 at what height will the pressure drop to (1/10) the value at the surface of the earth? d) This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.

Answer: (c) We know that - $ p={{p}_{0}}{{e}^{\left( -\frac{{{\rho }_{0}}gh}{{{p}_{0}}} \right)}} $ By substituting the known values, we can determine that h = 18.43 km (d) For $ \rho \alpha p $ to...

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a) Pressure decreases as one ascends the atmosphere. If the density of air is ρ, what is the change in pressure dp over a differential height dh? b) 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 ρo.

Answer: (a) The pressure falls as we ascend higher because the thickness of the gas above us diminishes. Let A be the cross-section of the air's horizontal layer, and dh be its height. The pressure...

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The surface tension and vapour pressure of water at 20oC is 7.28 × 10-2 N/m and 2.33 × 103 Pa, respectively. What is the radius of the smallest spherical water droplet which can form without evaporating at 20oC?

Answer: According to the question, the surface tension of water is T = 7.28 × 10-2 N/m and the vapour pressure is P = 2.33 × 103 Pa Let r represent the radius of the drop The excess pressure that is...

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If a drop of liquid breaks into smaller droplets, it results in lowering of the temperature of the droplets. Let a drop of radius R, break into N small droplets each of radius r. Estimate the drop in temperature.

Answer: The volume of a drop of liquid with a radius of R = (N) (volume of a liquid droplet of radius r) $ \frac{4}{3}\pi {{R}^{3}}=N\times \frac{4}{3}\pi {{r}^{3}} $ $ N=\frac{{{R}^{3}}}{{{r}^{3}}}...

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The free surface of the oil in a tanker, at rest, is horizontal. If the tanker starts accelerating the free surface will be titled by an angle θ. If the acceleration is a m/s2, what will be the slope of the free surface?

Answer: Let m be the mass of an elementary oil particle. The balancing forces are angled in the surface's direction. Pseudo force is given by ma mg represents the height of a small part of the oil...

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The sap in trees, which consists mainly of water in summer, rises in a system of capillaries of radius r = 2.5 × 10-5 m. The surface tension of sap is T = 7.28 × 10-2 N/m and the angle of contact is 0o. Does surface tension alone account for the supply of water to the top of all tress?

Answer: according to the question, the radius is r = 2.5 × 10-5 m The surface tension is T = 7.28 × 10-2 N/m It is also given that the angle of contact is θ = 0 degrees and the density is ρ = 103...

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A cubical block of density ρ is floating on the surface of the water. Out of its height L, fraction x is submerged in water. The vessel is in an elevator accelerating upwards with acceleration a. What is the fraction immersed?

Answer : Let ρ represent the density of a block and let height of the block be L Then, we can write the expression for the mass of the block as follows: m = Vρ = L3ρ Then, the weight of the block is...

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A cubical block of density ρ is floating on the surface of the water. Out of its height L, fraction x is submerged in water. The vessel is in an elevator accelerating upwards with acceleration a. What is the fraction immersed?

Answer : Let ρ represent the density of a block and let height of the block be L Then, we can write the expression for the mass of the block as follows: m = Vρ = L3ρ Then, the weight of the block is...

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A vessel filled with water is kept on a weighing pan and the scale adjusted to zero. A block of mass M and density ρ is suspended by a massless spring of spring constant k. This block is submerged inside into the water in the vessel. What is the reading of the scale?

Answer: We know that the upthrust of the block is equal to the weight of water displaced. The expression of which can be written as follows Vρwg Let x represent the compression in the spring. So,...

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The angle of contact at the interface of water-glass is 0o, ethyl alcohol-glass is 0o, mercury-glass is 140o, and methyl iodide-glass is 30o. A glass capillary is put in a trough containing one of these four liquids. It is observed that the meniscus is convex. The liquid in the trough is

a) water b) ethyl alcohol c) mercury d) methyl iodide Answer : The correct answer c) mercury If the contact angle is obtuse, the liquid meniscus in a capillary tube will be convex upwards. When one...

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In deriving Bernoulli’s equation, we equated the work done on the fluid in the tube to its change in the potential and kinetic energy. (a) What is the largest average velocity of blood flow in an artery of diameter 2 × 10–3 m if the flow must remain laminar? (b) Do the dissipative forces become more important as the fluid velocity increases? Discuss qualitatively.

Answer : Answer : (a) If dissipative forces exist, some forces in the liquid flow due to pressure difference are expended against dissipative forces, resulting in a high-pressure drop. (b) Due to...

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