GATE Engineering Sciences

For a laminar, incompressible, and fully-developed flow through a circular pipe, the ratio of the maximum velocity to the average velocity of the flow is

Air flows with a freestream velocity U over four different bodies having same frontal area facing the flow direction, as shown in the figure. Which one of the following bodies has...

Consider a steady, and incompressible flow over a body with characteristic length L. The boundary layer thickness at a distance x from the leading edge is δ. Which one of the follo...

Three different siphons steadily discharge water at velocities V₁, V₁₁, and V₁₁₁, as shown in the figure. The tubes of the siphons are of same diameter. If the frictional losses ar...

Consider the following statements: Assertion (a) Surface tension acts along the interface of two fluids. Reason (r) The pressure of the fluid inside a bubble is higher than that of...

The basic dimensions, i.e., mass, length, and time are represented by M, L, and T, respectively. The correct dimension of dynamic viscosity is

The velocity components in x- and y-directions of a two-dimensional, incompressible flow field are $u(x, y) = 2x^2 + y^3$ and $v(x, y) = x^3 – 2xy + f(x, y)$, respectively. Here, $...

Which of the following statements about streamlines, pathlines, and streaklines is/are correct?

A piezometer and a Pitot tube are tapped into a horizontal water pipe, as shown in the figure, where h₁ = 4 cm, h₂ = 6 cm and h₃ = 5 cm. Consider the flow to be steady, laminar, an...

A steady, laminar, and incompressible flow between a pair of infinite parallel plates is driven by a constant pressure gradient ($-dp/dx$). The plates are separated by a distance $...

An incompressible fluid flows between a pair of infinite plates separated by a distance L. The top plate is moving with a constant velocity U, whereas the bottom plate is stationar...

Consider two different cases of water flowing through a smooth pipe of 50 cm diameter. The mass flow rates for the two cases are (i) 0.25 kg.s⁻¹, and (ii) 0.8 kg.s⁻¹. Assume the de...

A two-dimensional source flow (with stream function, $\psi_1 = m \tan^{-1}\frac{y}{x}$) is placed at the origin in a uniform flow (with stream function, $\psi_2 = Uy$). Here, the s...

Consider a steady, laminar, and incompressible flow over a flat plate, as shown in the figure. With freestream velocity U∞ and kinematic viscosity v1, the boundary layer thickness...

A vertical jet of diameter $d_1$ strikes a horizontal plate with a velocity $U$, as shown in the figure. The plate has a hole of diameter $d_2(<d_1)$ concentric to the flow through...

The velocity of a fluid particle in a flow is given as: V = (a – x)î + (b + y)ĵ + (c + z)k where a, b, c are constants, and î, ĵ, k are unit vectors in x-, y-, z-directions, respec...

A gas is pressurized in a vertical frictionless piston-cylinder device, as shown in the figure. The piston has a mass of 4 kg and a cross-sectional area of 40 cm². A metallic block...

A ship is designed to sail at a speed of 8 m.s⁻¹. A designer makes a 1/10 scaled model to test the ship in a water tunnel. The model and the ship satisfy the dynamic similarity. Th...

A rectangular block (density = 600 kg.m⁻³) with base area of 0.06 m² and height 15 cm is partially submerged in water (density = 1000 kg.m⁻³), as shown in the figure. Assume accele...

For a steady, laminar, and incompressible flow over a flat plate, the local skin friction coefficient is given as Cf = $\frac{0.664}{\sqrt{Re_x}}$, where $Re_x$ is the local Reynol...

The axial velocity profile of a laminar, incompressible, and fully-developed flow in a circular pipe of radius R is given as $v_z = \frac{1}{4\mu} \frac{dp}{dz} (r^2 - R^2)$, where...

Air flows through a pipe of diameter D with an average velocity of 3 m.s⁻¹. The Darcy friction factor of the pipe is 0.02. Assume acceleration due to gravity as 10 m.s⁻². If the he...