Fluid Mechanics

Bernoulli's equation CANNOT be applied between

A quiescent fluid at temperature T3 is confined between two vertical parallel plates. While plate 1 is kept at temperature T1 and plate 2 is maintained at temperature T2, a velocit...

Water with a density of 1000 kg/m³ comes out of an industrial condenser through a horizontal pipe of 15 cm radius at the flow rate of 4.5 m³/min. The outlet of the pipe is connecte...

An inward flow reaction turbine, having an outer diameter of 1 m, runs at 600 RPM. The normal component of absolute velocity at the inlet is 10 m/s. If the guide blade angle is 15°...

Consider two identical tanks with a bottom hole of diameter d. One tank is filled with water and the other tank is filled with engine oil. The height of the fluid column h is same...

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...

A pitot tube connected to a U-tube mercury manometer measures the speed of air flowing in the wind tunnel as shown in the figure below. The density of air is 1.23 kg m⁻³ while the...

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

Consider a Pelton wheel of 1 m diameter. The magnitude of relative velocity of water at the bucket inlet is same as the magnitude of relative velocity of water at the bucket exit....

In the pipe network shown in the figure, all pipes have the same cross-section and can be assumed to have the same friction factor. The pipes connecting points W, N, and S with poi...

Air (density = 1.2 kg/m³, kinematic viscosity = 1.5×10⁻⁵ m²/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 the lead...

Consider incompressible laminar flow of a constant property Newtonian fluid in an isothermal circular tube. The flow is steady with fully-developed temperature and velocity profile...

The figure shows two fluids held by a hinged gate. The atmospheric pressure is P_a = 100 kPa. The moment per unit width about the base of the hinge is ________ kNm/m. (Rounded off...

For a two-dimensional, incompressible flow having velocity components u and v in the x and y directions, respectively, the expression $\frac{\partial(u^2)}{\partial x} + \frac{\par...

Which of the following is responsible for eddy viscosity (or turbulent viscosity) in a turbulent boundary layer on a flat plate?

A two dimensional flow has velocities in x and y directions given by u = 2xyt and v = -y^2t, where t denotes time. The equation for streamline passing through x = 1, y = 1 is

Water flows out from a large tank of cross-sectional area A₁ = 1 m² through a small rounded orifice of cross-sectional area A₀ = 1 cm², located at y = 0. Initially the water level,...

A cylindrical jet of water (density = 1000 kg/m³) impinges at the center of a flat, circular plate and spreads radially outwards, as shown in the figure. The plate is resting on a...

A high velocity water jet of cross section area = 0.01 m² and velocity = 35 m/s enters a pipe filled with stagnant water. The diameter of the pipe is 0.32 m. This high velocity wat...

Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabo...

Water flows through a pipe with a velocity given by $\vec{V} = (\frac{4}{t} + x + y)\hat{j}$ m/s, where $\hat{j}$ is the unit vector in the y direction, $t (> 0)$ is in seconds, an...

Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow...

Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, 2 m apart as shown bel...

A cube of side 100 mm is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is 800 kg/m³. Liquid of density 1000 kg/m³ is now p...

An idealized centrifugal pump (blade outer radius of 50 mm) consumes 2 kW power while running at 3000 rpm. The entry of the liquid into the pump is axial and exit from the pump is...

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 $\vec{V} = (5 + a_1x + b_1y)\hat{i} + (4 + a_2x + b_2y)\hat{j}$, where $a_1, b_1, a_2$ and $b_2$ are constants. Which one of th...

Water (density = 1000 kg/m³) at ambient temperature flows through a horizontal pipe of uniform cross section at the rate of 1 kg/s. If the pressure drop across the pipe is 100 kPa,...

A flat plate of width L = 1 m is pushed down with a velocity U = 0.01 m/s towards a wall resulting in the drainage of the fluid between the plate and the wall as shown in the figur...

The viscous laminar flow of air over a flat plate results in the formation of a boundary layer. The boundary layer thickness at the end of the plate of length L is δ. When the plat...

For a Pelton wheel with a given water jet velocity, the maximum output power from the Pelton wheel is obtained when the ratio of the bucket speed to the water jet speed is ________...

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

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 flow is...

For a steady flow, the velocity field is $\vec{V} = (-x^2 + 3y)\hat{i} + (2xy)\hat{j}$. The magnitude of the acceleration of a particle at $(1,-1)$ is

A tank open at the top with a water level of 1 m, as shown in the figure, has a hole at a height of 0.5 m. A free jet leaves horizontally from the smooth hole. The distance X (in m...

The arrangement shown in the figure measures the velocity V of a gas of density 1 kg/m³ flowing through a pipe. The acceleration due to gravity is 9.81 m/s². If the manometric flui...

A 60 mm-diameter water jet strikes a plate containing a hole of 40 mm diameter as shown in the figure. Part of the jet passes through the hole horizontally, and the remaining is de...

A sprinkler shown in the figure rotates about its hinge point in a horizontal plane due to water flow discharged through its two exit nozzles. The total flow rate Q through the spr...

A solid block of 2.0 kg mass slides steadily at a velocity V along a vertical wall as shown in the figure below. A thin oil film of thickness h = 0.15 mm provides lubrication betwe...

A test is conducted on a one-fifth scale model of a Francis turbine under a head of 2 m and volumetric flow rate of 1 m³/s at 450 rpm. Take the water density and the acceleration d...

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...

The Blasius equation related to boundary layer theory is a

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...

Match the following List-$${\rm I}$$ $$P.$$ Compressible flow $$Q.$$ Free surface flow $$R.$$ Boundary layer flow $$S.$$ Pipe flow $$T.$$ Heat convection List-$${\rm II}$$ $$U.$$ R...

A phenomenon is modeled using $$n$$ dimensional variables with $$k$$ primary dimensions. The number of non-dimensional variables is

A closed cylinder having a radius $$R$$ and height $$H$$ is filled with oil of density $$\rho .$$ If the cylinder is rotated about its axis at an angular velocity of $$\omega $$ ,...

Match List - $${\rm I}$$ with List - $${\rm II}$$ and select the correct answer using the code given below the Lists: List - $${\rm I}$$ $$A.$$ Grashof number $$B.$$ Schmid number...