List of top Fluid Mechanics Questions on Particle kinematics and dynamics asked in GATE XE

Which one of the following measures of viscosity is dimensionless?
Which one of the monomers given is used in the synthesis of cellulose?

A siphon is used to drain water (density } \(1000\,\text{kg/m}^3\) \(\textbf{}\) from a tank as shown. What is the maximum height \(z\) (in meters) of point C? Take \(g = 10\,\text{m/s}^2,\; p_A = 101\,\text{kPa},\; \text{vapour pressure } = 29.5\,\text{kPa},\;\)\(\text{and neglect friction.}\) (Round off to two decimal places)

Consider two-dimensional turbulent flow of air over a horizontal flat plate of length 1 m. Skin friction coefficient at a length $x$ from the leading edge is given by: \[ c_f = \frac{0.06}{(Re_x)^{0.2}} \] where $Re_x$ is the local Reynolds number. Find the drag force per unit width (in N/m$^2$) on the plate if the free stream velocity is 10 m/s. Density and dynamic viscosity of air are 1.2 kg/m$^3$ and $1.83 \times 10^{-5}$ Ns/m$^2$. (Round off to three decimal places)
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.

A two-dimensional Eulerian velocity field is given (in m/s) by \( \mathbf{V} = \left[ (\sqrt{5})x \right] \hat{i} - \left[ (\sqrt{12})y \right] \hat{j} \), where \( x \) and \( y \) are the coordinates (in meters) in a Cartesian coordinate system. The magnitude of the acceleration (in m/s\(^2\), up to one decimal place) of a fluid particle at \( x = 1 \, \text{m} \) and \( y = -1 \, \text{m} \) is \(\underline{\hspace{2cm}}\).