List of top Fluid Mechanics Questions asked in GATE Engineering Sciences

For an inviscid fluid with density \( \rho = 1 \, \text{kg/m}^3 \), the Cartesian velocity field is: \[ \mathbf{u} = (-2x + y)\mathbf{i} + (2x + y)\mathbf{j} \, \text{m/s} \] Neglecting body forces, find the magnitude of the pressure gradient (Pa/m) at \((x,y) = (1\,\text{m}, 1\,\text{m})\) at \( t = 1\,\text{s} \). (Round off to two decimal places)
A lawn sprinkler has horizontal arms of radius \( a = 10\,\text{cm} = 0.1\,\text{m} \). Water exits through jets of area \( A = 25\,\text{cm}^2 = 2.5\times10^{-3}\,\text{m}^2 \) with velocity \( V = 1\,\text{m/s} \). Each jet leaves orthogonal to the arm and makes a \( 60^\circ \) angle with the horizontal. Find the torque (N·m) required to hold the sprinkler stationary. (Round off to two decimal places).
A wooden cylinder (specific gravity = 0.6) of length $L$ and diameter $D$ floats in water (density 1000 kg/m$^3$). Find out the minimum value of $D/L$ for which the cylinder floats with its axis vertical. (Round off to three decimal places)
A cart of mass 10 kg is placed on a $60^\circ$ inclined plane. A turning vane (weight negligible) is mounted on the cart. A horizontal water jet from a 0.1 m$^2$ nozzle strikes the vane and is turned downward parallel to the inclined plane. Find the minimum jet velocity (m/s) so that the cart does not slide down. Neglect friction. Water density = 1000 kg/m$^3$, $g = 10$ m/s$^2$. (Round off to two decimal places)
A horizontal belt of negligible weight moves with velocity \(V = 2.5\,\text{m/s}\) over an oil film of depth \(h = 3\,\text{cm} = 0.03\,\text{m}\). The belt has length \(L = 2\,\text{m}\) and width \( b = 0.6\,\text{m} \). Find the viscosity of the oil (Pa·s) if minimum power required is 100 W. Neglect end effects. (Round off to two decimal places)
A 10 kg mass placed on an infinitely long horizontal massless flat platform is to be supported by a steady vertical water jet as shown in the figure. The diameter of the jet is 5 cm. What minimum average velocity is required to hold the mass in place?
Consider an inviscid flow through a smooth pipe which has a pitot-static tube arrangement as shown. Find the centre-line velocity in the pipe. Consider that the density of the fluid is 1000 kg/m\(^3\), acceleration due to gravity is 10 m/s\(^2\), and the specific gravity of the manometric fluid is 11.
The speed of propagation, \(c\), of a capillary wave depends on the density of the fluid, \(\rho\), the wavelength of the wave, \(\lambda\), and the surface tension, \(\sigma\). The dimensions are: \(\rho = ML^{-3}\), \(\lambda = L\), and \(\sigma = MT^{-2}\). Which expression is dimensionally correct?
A two-dimensional flow field is described by a combination of a source of strength \( m \) at the origin and a uniform flow \( U \) in the positive x-direction such that the velocity potential is given by \[ \phi = Ux + \frac{m}{2\pi} \ln \sqrt{x^2 + y^2} \] The stagnation streamline is shown in the figure. Find the distance \( aa' \).
A typical boundary layer over a flat plate has a linear velocity profile with zero velocity at the wall and freestream velocity \(U_{\infty}\) at the outer edge of the boundary layer. What is the ratio of the momentum thickness to the thickness of the boundary layer?
Identify the configuration(s) in which steady two-dimensional internal flow may show boundary layer separation if the flow direction is left to right.
Consider steady fully developed flow of a liquid through two large horizontal flat parallel plates separated by a distance of 2 mm. One of the plates is fixed and the other plate moves at a speed of 0.5 m/s. What is the magnitude of the pressure gradient (in Pa/m) in the direction of the flow required to ensure that the net flow through the plates is zero? Dynamic viscosity of the liquid is $5 \times 10^{-4}$ Ns/m$^2$ (Round off to the nearest integer)
The left-hand column lists some non-dimensional numbers and the right-hand column lists some physical phenomena. Indicate the correct combination.
As temperature increases:
Which of the following statement(s) regarding a venturimeter is/are correct?
Which of the following statement(s) is/are true for streamlines in a steady incompressible flow?
A flow has a velocity potential given by \( \phi = Ax^3 \) where ‘A’ is a non-zero constant. Which of the following statement(s) is/are true about the flow?
A boundary layer develops due to a two-dimensional steady flow over a horizontal flat plate. Consider a vertical line away from the leading edge which extends from the wall to the edge of the boundary layer. Which of the following quantity/quantities is/are not constant along the vertical line? \( u \) and \( v \) represent the components of velocity in the direction along the plate and normal to it, respectively, and \( x \) is taken along the length of the plate while \( p \) is the pressure.
A heavy horizontal cylinder of diameter D supports a mass of liquid having density ρ as shown in the figure. Find out the vertical component of force exerted by the liquid per unit length of the cylinder if g is the acceleration due to gravity.
The figure shows the developing zone and the fully developed region in a pipe flow where the steady flow takes place from left to right. The wall shear stress in the sections A, B, C, and D are given by \( \tau_A, \tau_B, \tau_C, \) and \( \tau_D \), respectively. Select the correct statement.