GATE Mechanical Engineering

In a laboratory experiment using a scaled down model to measure scour at a bridge pier, the Froude number is important. The ratio of the prototype length to the model length is 100...

For a fully-developed pipe flow, which of the following options is/are correct?

Consider a velocity field $\vec{V}=3 z \hat{i}+0 \hat{j}+C x \hat{k}$, where $C$ is a constant. if the flow is irrotational, the value of C is ________ (rounded off to 1 decimal pl...

The velocity field of a two-dimensional, incompressible flow is given by $\overrightarrow{V} = \ 2sin{h}\,x\,\hat{i} + v(x,y)\hat{j}$ where $ \hat{i}$ and $\underset{\dot{}}{j}$ de...

A liquid fills a horizontal capillary tube whose one end is dipped in a large pool of the liquid. Experiments show that the distance $L$ travelled by the liquid meniscus inside the...

Air (density = 1.2 kg/m 3 , kinematic viscosity = 1.5 × 10 -5 m 2 /s) flows over a flat plate with a free-stream velocity of 2 m/s. The wall shear stress at a location 15 mm from t...

The velocity field of a certain two-dimensional flow is given by V(𝑥, 𝑦) = 𝑘(𝑥𝑖̂ − 𝑦𝑗̂) where 𝑘 = 2 s -1 . The coordinates 𝑥 and 𝑦 are in meters. Assume gravitational eff...

Consider a unidirectional fluid flow with the velocity field given by V(𝑥, 𝑦, 𝑧, 𝑡) = 𝑢(𝑥, 𝑡) 𝑖̂ where 𝑢(0,𝑡) = 1. If the spatially homogeneous density field varies with...

A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero relative velocity with respect to the fluid. The velocity field in the fluid is $\vec V = (2x)...

In the following two-dimensional momentum equation for natural convection over a surface immersed in a quiescent fluid at temperature T ∞ (g is the gravitational acceleration, β is...

A solid spherical bead of lead (uniform density = 11000 kg/m 3 ) of diameter d = 0.1 mm sinks with a constant velocity V in a large stagnant pool of a liquid (dynamic viscosity = 1...

Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m 3 and 100 m/s, respectively....

A steady two-dimensional flow field is specified by the stream function ψ = kx 3 y, where x and y are in meters and the constant k = 1 m -2 s -1 . The magnitude of acceleration at...

The velocity field in a fluid is given to be $\vec{V}=(4xy)\hat{i}+2(x^2-y^2)\hat{j}$ Which of the following statement(s) is/are correct?

The steady velocity field in an inviscid fluid of density 1.5 is given to be $\vec{V}=(y^2-x^2)\hat{i}+(2xy)\hat{j} $ . Neglecting body forces, the pressure gradient at (x =1, y =...

Consider a laminar flow at zero over a flat plate . The shear stress at the wall is denoted by $${\tau _w}.$$ The axial positions $${x_1}$$ and $${x_2}$$ on the plate are measured...

Consider steady flow of an incompressible fluid through two long and straight pipes of diameters $${d_1}$$ and $${d_2}$$ arranged in series. Both pipes are of equal length and the...

For a steady flow, the velocity field is $$\overrightarrow V = \left( { - {x^2} + 3y} \right)\widehat i + \left( {2xy} \right)\widehat j.$$ The magnitude of the acceleration of the...

For 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 fol...

Consider the two-dimensional velocity field given by $$\overrightarrow V = \left( {5 + {a_1}x + {b_1}y} \right)\widehat i + \left( {4 + {a_2}x + {b_2}y} \right)\widehat j,$$ where...

For the stability of a floating body the

The velocity profile inside the boundary layer for flow over a flat plate is given as $${u \over {{U_\infty }}} = \sin \left( {{\pi \over 2}\,{y \over \delta }} \right),$$ where $$...

Consider fluid flow between two infinite horizontal plates which are parallel (the gap between them being $$50$$ $$mm$$). The top plate is sliding parallel to the stationary bottom...

For a two-dimensional flow, the velocity field is $$\overrightarrow u = {x \over {{x^2} + {y^2}}}\widehat i + {y \over {{x^2} + {y^2}}}\widehat j,$$ where $$\widehat i$$ and $$\wid...

The instantaneous stream-wise velocity of a turbulent flow is given as follows: $$$u\left( {x,y,z,t} \right) = \overline u \left( {x,y,z} \right) + \mu '\left( {x,y,z,t} \right)$$$...

Consider a fully developed steady laminar flow of an incompressible fluid with viscosity $$\mu $$ through a circular pipe of radius $$R.$$ Given that the velocity at a radial locat...

For a certain two-dimensional incompressible flow, velocity field is given by $$2xy\widehat i - {y^2}\widehat j.$$ The streamlines for this flow are given by the family of curves

The volume tric flow rate (per unit depth) between two streamlines having stream functions $${\psi _1}$$ & $${\psi _2}$$ is

For a floating body, buoyant force acts at the

Assuming constant temperature condition and air to be an ideal gas, the variation in atmospheric pressure with height calculated from fluid statics is

Air ( $${\rho = 1.2\,\,kg/{m^3}}$$ and kinematic viscosity, $${v = 2 \times {{10}^{ - 5}}{m^2}/s}$$ ) with a velocity of $$2m/s$$ flows over the top surface of a flat plate of leng...

A Prandtl tube (Pitot-static tube with $$C=1$$) is used to measure the velocity of water. The differential manometer reading is $$10$$ mm of liquid column with a relative density o...

Within a boundary layer for a steady incompressible flow, the Bernoulli equation

Couette flow is characterized by

If the fluid velocity for a potential flow is given by $$V\left( {x,y} \right) = u\left( {x,y} \right)i + v\left( {x,y} \right)j$$ with usual notations, then the slope of potential...

The head loss for a laminar incompressible flow through a horizontal circular pipe is $${h_1}$$. Pipe length and fluid remaining the same, if the average flow velocity doubles and...

Water $$\left( {\rho = 1000kg/{m^3}} \right)$$ flows through a venturimeter with inlet diameter $$80$$ $$mm$$ and throat diameter $$40$$ $$mm.$$ The inlet and throat gauge pressure...

Three parallel pipes connected at the two ends have flow-rates $$\,\,\,{Q_1},\,\,\,{Q_2},\,\,\,\,$$ and $${Q_3}$$ respectively, and the corresponding frictional head losses are $${...

For a fully developed laminar flow of water (dynamic viscosity $$0.001$$ $$Pa$$-s) through a pipe of radius $$5$$ $$cm,$$ the axial pressure gradient is $$-10$$ $$Pa/m$$. The magni...

Which of the following statement are TRUE, when the cavitation parameter $$\sigma = 0?$$ (i) The local pressure is reduced to vapor pressure. (ii) Cavitation starts (iii) Boiling o...

The velocity field on an incompressible flow is given by $$V = \left( {{a_1}x + {a_2}y + {a_3}z} \right)i + \left( {{b_1}x + {b_2}y + {b_3}z} \right)j$$ $$$ + \left( {{c_1}x + {c_2...

Consider fully developed flow in a circular pipe with negligible entrance length effects. Assuming the mass flow rate, density and friction factor to be constant, if the length of...

A fluid of dynamic viscosity $$2 \times {10^{ - 5}}\,\,kg/m.s$$ and density $$1kg/{m^3}$$ flows with an average velocity of $$1$$ $$m/s$$ through a long duct of rectangular $$\left...

Water flows through a pipe having an inner radius of $$10$$ $$mm$$ at the rate of $$36$$ $$kg/hr$$ at $${25^ \circ }C$$. The viscosity of water at $${25^ \circ }C$$ is $$0.001$$ $$...

For an incompressible flow field , $$\overrightarrow {V,} $$ which one of the following conditions must be satisfied?

For a completely submerged body with center of gravity $$'G'$$ and center of buoyancy $$'B',$$ the condition of stability will be

Water flows through a $$10$$ $$mm$$ diameter and $$250$$ $$m$$ long smooth pipe at an average velocity of $$0.1$$ $$m/s.$$ The density and the viscosity of water are $$997kg/{m^3}$...

Consider laminar flow of water over a flat plate of length $$1$$ $$m.$$ If the boundary layer thickness at a distance of $$0.25$$ $$m$$ from the leading edge of the plate is $$8$$...

The difference in pressure (in $$N/{m^2}$$) across an air bubble of diameter $$0.001$$ $$m$$ immersed in water (surface tension $$ = 0.072$$ $$N/m$$) is _____________.

Consider the following statements regarding streamline(s): (i) It is a continuous line such that the tangent at any point on it shows the velocity vector at that point (ii) There i...

A flow field which has only convective acceleration is

Consider a velocity field $$\overrightarrow V = K\left( {y\widehat i + x\widehat k} \right),$$ where $$K$$ is a constant. The vorticity, $${\Omega _z},$$ is

For a completely submerged body with centre of gravity $$‘G’$$ and centre of buoyancy $$‘B’,$$ the condition of stability will be

An ideal water jet with volume flow rate of $$0.05{m^3}/s$$ strikes a flat plane placed normal to its path and exerts a force of $$1000N.$$ Considering the density of water as $$10...

In a simple concentric shaft-bearing arrangement, the lubricant flows in the $$2$$ $$mm$$ gap between the shaft and the bearing. The flow may be assumed to be a plane Couette flow...

For a fully developed flow of water in a pipe having diameter $$10$$ $$cm,$$ velocity $$0.1$$ $$m/s$$ and kinematic viscosity $${10^{ - 5}}\,\,{m^2}/s,$$ the value of Darcy frictio...

A flow field which has only convective acceleration is

Consider the turbulent flow of a fluid through a circular pipe of diameter, $$D.$$ Identify the correct pair of statements. $${\rm I}.$$ The fluid is well-mixed $${\rm II}.$$ The f...

For steady, fully developed flow inside a straight pipe of diameter $$D,$$ neglecting gravity effects, the pressure drop $$\Delta p$$ over a length $$L$$ and the wall shear stress...

Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is $$20$$ $$mm$$ with uniform velocity of $$2$$ $$m/s.$$ Acceleration due to...

An incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is $$1mm$$ at a location where the Reynolds number is $$1000$$. If the vel...

A streamline and an equipotential line in a flow field

For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?

Velocity vector of a flow fields is given as $$\overrightarrow V = 2xy\widehat i - {x^2}z\widehat j.$$ The vorticity vector at $$(1,1,1)$$ is

A smooth pipe of diameter $$200$$ $$mm$$ carries water. The pressure in the pipe at section $${S_1}\,\,$$ (elevation : $$10$$ $$m$$ ) is the $$50$$ $$kPa.$$ At section $${S_2}\,\,$...

A lightly loaded full journal bearing has a journal of $$50mm,$$ bush bore of $$50.50mm$$ and bush length of $$20mm.$$ if rotational speed of journal is $$1200rpm$$ and average vis...

Maximum velocity of a one-dimensional incompressible fully developed viscous flow, between two fixed parallel plates, is $$6\,\,m{s^{ - 1}}.$$ Then mean velocity (in $$m{s^{ - 1}}$...

You are asked to evaluate assorted fluid flows for their suitability in a given laboratory application. The following three flow choices. Expressed in terms of the two - dimensiona...

Consider steady, incompressible and irrotational flow through a reducer in a horizontal pipe where the diameter is reduced from $$20cm$$ to $$10cm.$$ The pressure in the $$20cm$$ p...

Water at $${25^0}C$$ is flowing through a $$1.0km$$ long $$G.I.$$ pipe of $$200mm$$ diameter at the rate of $$0.07$$ $${m^3}/s.$$ If value of Darcy friction factor for this pipe is...

For a continuity equation given $$\nabla .\overrightarrow V = 0$$ to be valid, $$\overrightarrow V $$ where is the velocity vector, which one of the folllowing is a necessary condi...

A two dimensional fluid element rotates like a rigid body. At a point with in the element, the pressure is $$1$$ unit. Radius of the Mohr's circle, charactering the state of stress...

A journal bearing has a shaft diameter of $$40$$ $$mm$$ and a length of $$40mm.$$ The shaft is rotating at $$20$$ $$rad/s$$ and the viscosity of the lubricant is $$20$$ $$mPa$$-$$s...

Consider steady laminar incompressible axi-symmetric fully developed viscous flow through a straight circular pipe of constant cross - sectional area at a Reynolds number of $$5.$$...

Newton's law of viscosity states that the shear stress in a fluid is proportional to :

In a steady flow through a nozzle, the flow velocity on the nozzle axis is given by $$u = {u_0}\left( {1 + 3x/L} \right),\,\,$$ where $$x$$ is the distance along the axis of the no...

Oil flows through a $$200mm$$ diameter horizontal cast iron pipe (friction factor, $$f=0.0225$$) of length $$500m.$$ The volumetric flow rate is $$0.2{m^3}/s.$$ The head loss (in $...

Which combination of the following statements about steady incompressible forced vortex flow is correct? P: Shear stress is zero at all points in the flow. Q: Velocity is directly...

Consider an incompressible laminar boundary layer flow over a flat plate of length $$L$$, aligned with the direction of an incoming uniform free stream. If $$F$$ is the ratio of th...

Oil in a hydraulic cylinder is compressed from an initial volume $$2{m^3}$$ to $$1.96{m^3}$$. If the pressure of oil in the cylinder changes from $$40$$ $$MPa$$ to $$80$$ $$MPa$$ d...