List of top Fluid Mechanics Questions on Compressible and Incompressible Fluids asked in GATE Engineering Sciences

For a steady and incompressible flow, the velocity field $\vec{V}$ in Cartesian $(x,y,z)$ coordinate system is given as: \[ \vec{V} = 5x \, \mathbf{i} - P y \, \mathbf{j} + 3 \mathbf{k}. \] Here, $\mathbf{i}, \mathbf{j}, \mathbf{k}$ are unit vectors along $x, y, z$ directions, respectively, and $P$ is a constant. Which one of the following options is the correct value of $P$ that satisfies the conservation of mass for the given velocity field?
A ship is to be operated in a fluid medium with kinematic viscosity $0.032 \times 10^{-3} \, \text{m}^2/\text{s}$. A one-tenth scale model of the ship is built for testing. Consider, inertia, viscous, and gravity forces are dominant for the ship and its model during the operation. The required kinematic viscosity of the liquid for testing the model is $P \times 10^{-6} \, \text{m}^2/\text{s}$. Find $P$ (rounded off to 2 decimal places).

An oil of density $870 \,\text{kg/m}^3$ and viscosity $0.036 \,\text{Pas}$ flows through a straight pipe of 10 cm diameter and 1.5 km length at the flow rate of 250 liters per minute under steady and incompressible flow conditions. To control the flow rate of oil, a valve is fixed at the middle of the pipe causing no change in the total length of the pipe. The total head loss measured across the two ends of the pipe is 11.60 m. Using gravitational acceleration as $10 \,\text{m/s}^2$, the minor head loss contributed by the presence of the valve in m (rounded off to 2 decimal places) is ...............

Consider, a kite weighing 100 grams as essentially a rigid flat plate making an angle 8° with the horizontal and having a planform area of 0.045 m$^2$ when exposed to horizontal parallel wind of 60 km/h. The thread string of the kite makes an angle 45° with the horizontal. A tension of 450 grams in the thread is necessary to float the kite steadily. Take air density as 1.2 kg/m$^3$ and gravitational acceleration as 9.81 m/s$^2$. The lift coefficient $(C_L)$ associated with the air flow around steadily floating kite (rounded off to 2 decimal places) is ....................
Driven by a pressure gradient of 100 kPa/m, a fluid of dynamic viscosity 0.1 Pa·s flows between two fixed infinitely large parallel plates under steady, incompressible, and fully developed laminar conditions. The average velocity of the flow is 2 m/s. The gap between the parallel plates in mm (rounded off to 2 decimal places) is ............
An incompressible fluid is flowing between two infinitely large parallel plates separated by 5 mm distance. The bottom plate is stationary and the top plate is moving at a constant velocity of 5 mm/s in the direction parallel to the bottom plate. The flow of the fluid between the plates is steady, two-dimensional, laminar, and the variation of fluid velocity is linear between the plates. A square fluid element of 1 mm side is considered at equal distance from both the plates in the flow field such that one of its sides is parallel to the plates. The magnitude of circulation in mm$^2$/s (in integer) along the edges of the square fluid element is .................
A fixed control volume has four one-dimensional boundary sections (1, 2, 3, and 4). For a steady flow inside the control volume, the flow properties at each section are tabulated below:
The rate of change of energy of the system which occupies the control volume at this instant is $E \times 10^6$ J/s. Find the value of $E$ (rounded off to 2 decimal places).
Water flows through a pipe of diameter 20 cm at a flow rate of 0.025 m$^3$/s. A pitot-static tube is placed at the centre of the pipe and indicates the pressure difference of 5 cm of water column. Theoretical velocity measured through pitot-static tube when multiplied with velocity coefficient $C_V$ gives the actual velocity of the flow. If the mean velocity in the pipe is 90% of the actual velocity at the centre of the pipe and the gravitational acceleration is 10 m/s$^2$, find $C_V$ (rounded off to 2 decimal places).
A liquid flows under steady and incompressible flow conditions from station 1 to station 4 through pipe sections P, Q, R, and S as shown in figure. Consider, $d, V$, and $h$ represent the diameter, velocity, and head loss, respectively, in each pipe section with subscripts ‘P’, ‘Q’, ‘R’, and ‘S’. $\Delta h$ represents the head difference between the inlet (station 1) and outlet (station 4). All the pipe sections are placed on the same horizontal plane for which the figure shows the top view.
Which one of the following options is correct for the given flow loop?
Consider, $\mathbf{i}$ and $\mathbf{j}$ are unit vectors along $x$ and $y$ directions of a Cartesian $(x,y)$ coordinate system; respectively and $t$ is time. Temperature $(T)$ and fluid velocity $(\vec{V})$ are given for a flow field as: \[ T = x^2 + y t + 35 \] \[ \vec{V} = (4xy)\mathbf{i} + (xt - 2y^2)\mathbf{j} \] The total rate of change of temperature in the flow field (in integer) for time $t=2$ at a point $(2,3)$ is ............
Consider the steady, incompressible, and fully developed laminar flow of a fluid through a circular pipe. Here, $\Delta P$ is the pressure drop in the direction of the flow and $V$ is the average axial velocity of the fluid at any cross-section. The relation between $\Delta P$ and $V$ is: \[ \Delta P = K V^n \] Here, $K$ and $n$ are constants. Which one of the following options is the correct value of $n$?
A doublet is the resulting flow pattern when a sink and a source of equal strength are brought together. Which one of the following options correctly represents the nature of the product of the strength and the distance between them during approach?

Figure shows two parallel plates (upper plate at $x=b$ and lower plate at $x=-b$) of length $L$ (aligned in $z$ direction) and infinite width (in $y$ direction, normal to the plane of figure). Two immiscible, incompressible liquids are flowing steadily in the $z$ direction through the thin passage between the plates under the influence of horizontal pressure gradient $\dfrac{(P_0-P_L)}{L}$. During the flow, the passage is always half-filled with denser fluid I (viscosity $\mu'$) at the bottom and rest is occupied by lighter fluid II (viscosity $\mu''$; $\mu''<\mu'$). Considering exactly planar interface between the fluids and no instabilities in the flow, the shear stress $\tau_{xz}$ is expressed as: \[ \tau_{xz} = \frac{(P_0 - P_L)b}{L}\left(\frac{x}{b} - \frac{1}{2}\frac{\mu' - \mu''}{\mu' + \mu''}\right). \] Which one of the following options correctly identifies the location of the point having maximum velocity of the flow?

Group-I shows different two-dimensional bodies and Group-II mentions their total drag coefficient $(C_D)$ based on frontal area while facing parallel flow of fluid having Reynolds number $Re \geq 10^4$ along the direction of arrow. The bodies are placed symmetrically with respect to the flow direction.
Which one of the following options identifies the correct match between Group-I and Group-II, as per the concept of degree of streamlining?
Figure shows the steady and incompressible flow of a fluid in the direction of arrow from section A to section D. Three pipe connectors are to be placed between sections at A and D having Total Energy Line (TEL) and Hydraulic Grade Line (HGL) as depicted in the figure. Consider, $g, P, Q, V, \gamma$, and $Z$ denote gravitational acceleration, pressure, volume flow rate, velocity, specific weight, and elevation of centerline of the pipe connectors from the datum, respectively.
Which one of the following options, in sequence, indicates the correct nature of connectors between sections A and B, B and C, and C and D in the direction of flow?
A solid body of uniform specific gravity floats in a deep liquid pool. Take $B, G$, and $M$ as the centre of buoyancy, centre of gravity, and metacentre of the body, respectively. Which one of the following options is correct for the stable floatation of the body in the pool when the body is given a small tilt angle?
Statement of Reynolds Transport Theorem is given below with three blanks: The rate of change of ____________ extensive property can be calculated by summing the rate of change of the amount of same property in the ____________ and the rate at which the property is ____________ the surface of the control volume. Which one of the following options correctly fills the blanks by using its comma-separated phrases in sequence?
Conservation of mass for a steady axisymmetric flow field in the cylindrical $(r,z)$ coordinates is: \[ \frac{1}{r}\frac{\partial (rV_r)}{\partial r} + \frac{\partial V_z}{\partial z} = 0. \] Here, $V_r$ and $V_z$ are the radial and axial components of velocity, respectively. Which one of the following options is correct if $\psi$ is the stream function?
A sharp flat plate of length $L$ and infinite width is immersed parallel to a fluid stream having velocity $u_\infty$. At a point on the plate, far away from the leading edge and not near the trailing edge, the boundary layer thickness, the displacement thickness, and the momentum thickness are denoted as $\delta$, $\delta^*$, and $\theta$, respectively. Which one of the following options correctly represents the relation between these thicknesses?
Consider the following Statements [1] and [2].
Statement [1]: The Eulerian study focusses attention on individual particle and its motion is observed as a function of time.
Statement [2]: The Lagrangian study focusses attention on the motion of the particles passing through an identified point.
Which one of the following options identifies the correctness of the given statements?
Group-I indicates different properties of fluid and Group-II defines their basic dimensions in terms of Force (F), Length (L), and Time (T).
Which one of the following options identifies the correct match between Group-I and Group-II?
Fluid at a constant flow rate passes through a long, straight, cylindrical pipe that has an axisymmetric convergent section at the end. Which one of the following options correctly represents the velocity field in the converging section in cylindrical $(r,\theta,z)$ coordinates?
A stationary circular pipe of radius $R = 0.5$ m is half filled with water (density = 1000 kg/m$^3$), whereas the upper half is filled with air at atmospheric pressure, as shown in the figure. Acceleration due to gravity is $g = 9.81$ m/s$^2$. The magnitude of the force per unit length (in kN/m, rounded off to one decimal place) applied by water on the pipe section AB is $________________$.
Axial velocity profile $u(r)$ for an axisymmetric flow through a circular tube of radius $R$ is given as, \[ \frac{u(r)}{U} = \left(1 - \frac{r}{R}\right)^{1/n} \] where $U$ is the centerline velocity. If $V$ refers to the area-averaged velocity (volume flow rate per unit area), then the ratio $V/U$ for $n = 1$ (rounded off to two decimal places) is $________________$.
A hydraulic turbine with rotor diameter of 100 mm produces 200 W of power while rotating at 300 rpm. Another dynamically-similar turbine rotates at a speed of 1500 rpm. Consider both turbines to operate with the same fluid (identical density and viscosity), and neglect any gravitational effect. Then the power (in W, rounded off to nearest integer) produced by the second turbine is $________________$.