Which one of the following combinations of elementary flows will lead to an ideal flow past a deeply submerged circular cylinder with circulation?
Show Hint
- Source, sink and uniform flow
- Doublet, uniform flow and vortex
- Doublet and vortex
- Source and uniform flow
The Correct Option is B
Solution and Explanation
To introduce circulation around the cylinder (i.e., lifting flow, Kutta–Joukowski effect), a vortex must be added to the combination.
Thus, the required elementary flows are:
1. Doublet → represents the cylinder.
2. Uniform flow → represents the free-stream motion.
3. Vortex → introduces circulation around the cylinder.
Therefore, the correct combination is Doublet + Uniform flow + Vortex, which corresponds to Option (B).
Top Questions on Fluid Mechanics
- Consider the flowsheet in the figure for manufacturing C via the reaction \( A + B \rightarrow C \) in an isothermal CSTR. The split in the separator is perfect so that the recycle stream is free of C and the product stream is pure C. Let \( x_i \) denote the mole fraction of species \( i \) (where \( i = A, B, C \)) in the CSTR, which is operated in excess B with \( x_B/x_A = 4 \). The reaction is first-order in A with the reaction rate \( (-r_A) = k x_A \), where \( k_x = 5.0 \, {kmol}/({m}^3 \cdot {h}) \). The reactor volume \( V \) in \( {m}^3 \) is to be optimized to minimize the cost objective \( J = V + 0.25 R \), where \( R \) is the recycle rate in \( {kmol/h} \). For a product rate \( P = 100 \, {kmol/h} \), the optimum value of \( V \) is ____ \( {m}^3 \) (rounded off to the nearest integer). Given: \[ \frac{d}{dz} \left( \frac{z}{(1-z)^2} \right) = \frac{1}{(1 - 2z)^2} \]
- An adiabatic pump of efficiency 40% is used to increase the water pressure from 200 kPa to 600 kPa. The flow rate of water is 600 L/min. The specific heat of water is 4.2 kJ/(kg°C). Assuming water is incompressible with a density of 1000 kg/m³, the maximum temperature rise of water across the pump is \_\_\_\_°C (rounded off to 3 decimal places).
An electrical wire of 2 mm diameter and 5 m length is insulated with a plastic layer of thickness 2 mm and thermal conductivity \( k = 0.1 \) W/(m·K). It is exposed to ambient air at 30°C. For a current of 5 A, the potential drop across the wire is 2 V. The air-side heat transfer coefficient is 20 W/(m²·K). Neglecting the thermal resistance of the wire, the steady-state temperature at the wire-insulation interface __________°C (rounded off to 1 decimal place).
GIVEN:
Kinematic viscosity: \( \nu = 1.0 \times 10^{-6} \, {m}^2/{s} \)
Prandtl number: \( {Pr} = 7.01 \)
Velocity boundary layer thickness: \[ \delta_H = \frac{4.91 x}{\sqrt{x \nu}} \]- Water flows through a horizontal pipe with a velocity of 2 m/s. The cross-sectional area of the pipe reduces to half. What is the velocity of water in the narrower section?
- BITSAT - 2025
- Physics
- Fluid Mechanics
Consider two identical tanks with a bottom hole of diameter \( d \). One tank is filled with water and the other tank is filled with engine oil. The height of the fluid column \( h \) is the same in both cases. The fluid exit velocity in the two tanks are \( V_1 \) and \( V_2 \). Neglecting all losses, which one of the following options is correct?
Questions Asked in GATE NM exam
- If \( P e^x = Q e^{-x} \) for all real values of \( x \), which one of the following statements is true?
Bird : Nest :: Bee : __________
Select the correct option to complete the analogy.- Consider the function \( f(x) = |x| - 1 \). Which of the following statements is/are true in the interval \([-10, 10]\)?
- GATE NM - 2025
- Continuity and differentiability
A closed system is undergoing a reversible process 1–P–2 from state 1 to 2, as shown in the figure, where X and Y are thermodynamic properties. An irreversible process 2–Q–1 brings the system back from 2 to 1. The net change in entropy of the system and surroundings during the above-mentioned cycle are _______ respectively.
- GATE NM - 2025
- Thermodynamics
A ship of 3300 tonne displacement is undergoing an inclining experiment in seawater of density 1025 kg/m\(^3\). A mass of 6 tonne is displaced transversely by 12 m as shown in the figure. This results in a 0.12 m deflection of a 11 m long pendulum suspended from the centerline. The transverse metacenter of the ship is located at 7.25 m above the keel.
The distance of the center of gravity from the keel is ________ m (rounded off to two decimal places).
- GATE NM - 2025
- Ship Dynamics