Mechanical Properties of Fluids
Mechanical Properties of Fluids
- The excess pressure inside a soap bubble of radius 2 cm is (surface tension of soap solution = 0.03 N/m) Answer: C. 6 Pa A soap bubble has two surfaces: Δ P=4T/r=4×0.03/0.02=6 Pa. 1
- Eight identical rain drops, each falling with terminal velocity \(v\), coalesce to form a single drop. The terminal velocity of the big drop is Answer: A. 4v Volume conserved: R³=8r³⇒ R=2r . Since v_t∝ r² , new terminal velocity =4v . 1
- Water flows through a horizontal pipe whose cross-sectional area at a wide section is twice that at a narrow section. If the speed at the wide section is 2 m/s, the pressure difference between the wide and narrow sections is (density of water = 1000… Answer: C. 6000 Pa Continuity: v₂=2×2=4 m/s. Bernoulli: Δ P=1/2ρ(v₂²-v₁²)=500(16-4)=6000 Pa. 1
- In Bernoulli’s theorem, which of the following is conserved? (A) linear momentum (B) angular momentum (C) mass (D) energy In Bernoulli’s theorem, Energy is conserved 2
- A rectangular wire frame of size 2 cm x 2 cm, is dipped in a soap solution and taken out. Answer: 3x10⁻⁵ J or 30μJ Explaination: A2=3x3=9 and A1= 2x2=4 Area are in cm² let convert it to m² A2=9x10⁻⁴ and A1=4x10⁻⁴ , T=3x10⁻² The ex... 1
- How much work is required to form a bubble of 2 cm radius from the soap solution having surface tension 0.07 N/m. Answer= 0.703× 10-3 J \ \ \ or \ \ \ 7.038× 10⁻⁴ J Explaination:: Given:: Radius of the bubble = 2 cm or 0.02 m Surface tension = 0.07 N/m S... 1
- A drop of mercury of radius 0.2 cm is broken into 8 droplets of the same size. Find the work done if the surface tension of mercury is 435.5 dyne/cm Answer:: 2.19 x 10⁻⁵ J Explaination:: Given :: R = 0.2 cm, n = 8, T = 435.5 dyn/cm As the volume of the liquid remains constant, volume of n... 1
- Twenty seven droplets of water, each of radius 0.1 mm coalesce into a single drop. Find the change in surface energy. Surface tension of water is 0.072 N/m. Correct answer = 1.628 x 10⁻⁷ J Explaination :: Given :: r=0.1mm =0.1 x 10⁻³m , T=0.072 N/m Let R be the radius of the single drop formed du... 1
- An air bubble of radius 0.2 mm is situated just below the water surface. Calculate the gauge pressure. Surface tension of water = 7.2x 10-2 N/m. Correct Answer: 720 N/m² Explaination:: Given : Radius of bubble =0.2 mm = 2× 10⁻⁴ m , surface tension of water = 0.072 N/m = 720× 10⁻⁴ N/m... 1
- Calculate the rise of water inside a clean glass capillary tube of radius 0.1 mm, when immersed in water of surface tension 7x10-2 N/m. Correct Answer = 0.142 m Explaination Given:: r = 0.1 mm = 10⁻⁴ m, T = 7 × 10⁻² N/m, θ = 0°, ρ = 1000 kg/m³, g = 9.8 m/s^(2 ) To find: Heigh... 1
- The pressure of water inside the closed pipe is 3 x105 N/m2. This pressure reduces to 2x105 N/m2 on opening the value of the pipe. Correct answer = 14.14 m/s Explaination:: Given:: p₁ = 3 × 10⁵ Pa, v₁ = 0, p₂ = 2 × 10⁵ Pa, ρ = 10³ kg/m³ Assuming the potential head to be... 1
- With what velocity does water flow out of an orifice in a tank with gauge pressure 4 x105 N/m2 before the flow starts? Correct answer= 28.28 m/s Explaination Given:: p - p₀ = 4 × 10⁵ Pa, ρ = 10³ kg/m³ If the orifice is at a depth h from the water surface in a... 1
- The speed of water is 2m/s through a pipe of internal diameter 10 cm. Correct answer =7.07 x 10⁻² m Explaination:: Given : d1=10cm =0.1 m , v1=2m/s, v2=4m/s Solution: by the equation of continuity , the ratio o... 1
- With what terminal velocity will an air bubble 0.4 mm in diameter rise in a liquid of viscosity 0.1 Ns/m2 and Answer= - 0.782 × 10^(-3 )m/s (upwards) Given: d=0.4 mm, r=d/2 = 0.2mm= 2×10⁻⁴ m, , h = 0.1 Pa-s, p_L = 0.9 × 10³ kg/m^(3 )= 900 kg/m³, ^( )... 1
- A horizontal force of 1 N is required to move a metal plate of area 10-2 m2 with a velocity of Correct answer= 7.5 Ns/m² Explaination:: Given : F=1, A=10⁻² m^(2, )v_(0 )=2 × 10⁻² m/s, y=1.5 × 10⁻³ m Solution: Velocity gradient, dv/dy =... 1
- Calculate the viscous force acting on a rain drop of diameter 1 mm, falling with a uniform velocity 2 m/s through air. Correct answer = 3.394 ×10^(-7 )N or 3.393 ×10^(-7 )N Explaination:: Given: d= 1 mm, v_(0 )= 2 m/s, η= 1.8 × 10⁻⁵ Ns/m² r =d/2 =0.5 mm = 5 ×... 1
- In a hydraulic lift, the input piston had surface area 30 cm2 and the output piston has surface area of 1500 cm2. Correct answer = 1250 N Explaination:: Given : A_(1 )= 30 cm^(2 )= 3×10⁻³ m² , A₂ = 1500 cm^(2 )= 0.15 m^(2 )F₁=25 N By Pascal’s law F1/A1=F... 1
- Find the pressure 200 m below the surface of the ocean if pressure on the free surface of liquid is one atmosphere Correct Answer= 21.789×10^(5 )N/m² Explaination:: Given : h=200 m, ρ=1060 kg/m^(3 )p_(0 )= 1.013×10^(5 )Pa, g = 9.8 m/s² Absolute pressure,... 1
- Derive an expression for capillary rise for a liquid having a concave meniscus. Consider a capillary tube of radius r partially immersed into a wetting liquid of density p. Let the capillary rise be h and q be the angle... 1
- Explain the capillary action When a capillary tube is partially immersed in a wetting liquid, there is a capillary rise and the liquid meniscus inside the tube is concav... 1
- Obtain an expression for conservation of mass starting from the equation of continuity. Consider a fluid in steady or streamline flow, that is its density is constant. The velocity of the fluid within a flow tube, while everywhe... 1
- Derive an expression of excess pressure inside a liquid drop . Consider a spherical drop of radius R and surface tension T Let p_i be the pressure inside the drop and p₀ be the pressure outside it. As th... 1
- Why does the speed of a liquid increase and its pressure decrease when a liquid passes through constriction in a horizontal pipe? Consider a horizontal constricted tube. Let A_(1 )and A₂ be the cross-sectional areas at points P₁ and P₂, respectively. Let v₁ and v₂ be th... 1
- Why does velocity increase when water flowing in broader pipe enters a narrow pipe? When a tube narrows, the same volume occupies a greater length, as schematically shown in Fig. A₁ is the cross section of the broader pipe a... 1