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The velocity field in Cartesian coordinates in a two-dimensional steady incompressible flow of a fluid with density ρ is V = xi − yj. Assuming no body and line forces, the magnitude of pressure gradient ∇p at point (1,1) is0 AnswerA two-dimensional, incompressible fluid flow is described by the stream function Ψ = xy 3 m2 /s on the Cartesian x-y plane. If the density and dynamic viscosity of the fluid are 1 kg/m3 and 0.1 kg/m-s, respectively, the magnitude of the pressure gradient in the x direction at x=1 m and y=1 m is _______ N/m3 (round off to 1 decimal place).0 AnswerA two-dimensional incompressible frictionless flow field is given by ˆ ˆ u x y i j . If is the density of the fluid, the expression for pressure gradient vector at any point in the flow field is given as0 AnswerA two-dimensional velocity field in Cartesian coordinates is defined by V = yi − xj. This flow is0 AnswerC onsider a fully developed, two-dimensional and steady flow of a viscous fluid between two fixed parallel plates separated by a distance of 30 mm. The dynamic viscosity of the fluid is 0.01 kg/m-s and the pressure drop per unit length is 300 Pa/m. The fluid velocity at a distance of 10 mm from the bottom plate, in m/s, is ________.0 AnswerT he velocity field in a two-dimensional, unsteady flow is given by V(x, y, t) 2xy2 iˆ 3xyt ˆj m/s. The magnitude of acceleration of a fluid particle located at x = 1 m, y = 1 m at the time t = 1 s, in m/s2, is0 AnswerTwo immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, 2 m apart as shown below. The bottom plate is fixed and the upper plate moves to the right with a constant velocity of 3 m/s. With the assumptions of Newtonian fluid, steady, and fully developed laminar flow with zero pressure gradient in all directions, the momentum equations simplify to0 AnswerI n a two-dimensional, incompressible and irrotational flow, fluid velocity (v) in the ydirection is given by v 2x5y . The velocity (u) in the x-direction is0 AnswerA nalysis of a flow phenomenon in a system requires the following variables: i. Pressure [M L1 T 2] ii. Velocity of the fluid [L T 1] iii. Size of the system [L] iv. Density of the fluid [M L3] v. Viscosity of the fluid [M L1 T 1] According to Buckingham Pi theorem (dimensional analysis) what is the number of independent DIMENSIONLESS variables needed to describe this system?1 AnswerIf the stream function ( ( , ) xy ) for a two-dimensional incompressible flow field is given as 2 2 2y x y , the corresponding velocity field is0 AnswerThe drag force, FD, on a sphere kept in a uniform flow field depends on the diameter of the sphere, D; flow velocity, V; fluid density, ρ; and dynamic viscosity, µ. Which of the following options represents the non-dimensional parameters which could be used to analyze this problem? - gate civil 2017 1 AnswerIn a Lagrangian system, the position of a fluid particle in a flow is described as x = xoe −kt and y = yoe kt where t is the time while xo, yo, and k are constants. The flow is (Gate 2018 Mechanical engineering)0 AnswerFor a two-dimensional incompressible flow field given by u Axi ˆ y ˆ j , where A 0 , which one of the following statements is FALSE? (Gate 2018 Mechanical engineering)0 AnswerAn incompressible Newtonian fluid flows in a pipe of diameter D1 at volumetric flow rate Q . Fluid with same properties flows in another pipe of diameter 2 1 D D / 2 at the same flow rate Q . The transition length required for achieving fully-developed flow is 1 l for the tube of diameter D1 , while it is 2 l for the tube of diameter D2 . Assuming steady laminar flow in both cases, the ratio 1 2 l l is:0 AnswerI f 2 2 2( ) u x y and v axy represent the x- and y-components of the two-dimensional velocity field of an incompressible flow, the value of the constant a is ______0 AnswerThe inviscid, incompressible flow field resulting from a uniform flow past a circular cylinder of radius R centered at the origin is given by:0 AnswerFor steady flow of a viscous incompressible fluid through a circular pipe of constant diameter, the average velocity in the fully developed region is constant. Which one of the following statements about the average velocity in the developing region is TRUE?1 AnswerAt 30°N and 700 hPa pressure level, wind field is in gradient balance. If the gradient wind speed is 50 m s–1 and radius of curvature of the flow is 50 km, the corresponding geostrophic wind speed is __________ m s–1. (Give the answer to one decimal place.) Take the angular velocity of the Earth as 7.3x10–5 s–10 AnswerA cylindrical pipeline of length 30 km is transporting naphtha. Pressure sensors are attached along pipe length to detect leaks. Gate-2018-General-Aptitude0 AnswerBernoulli’s equation is applicable for (GATE-CIVIL-Engg-2018)2 Answer
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