List of top Fluid Mechanics and Mechanical Operations Questions

Water of density 1000 kg/m³ is pumped at a volumetric flow rate of \( 3.14 \times 10^{-2} \) m³/s through a pipe of inner diameter 10 cm and length 100 m, from a large Reservoir 1 to another large Reservoir 2 at a height of 50 m above Reservoir 1, as shown in the figure. The flow in the pipe is in the turbulent regime with a Darcy friction factor \( f = 0.06 \) and a kinetic energy correction factor \( \alpha = 1 \). Take \( g = 9.8 \) m/s². If all minor losses are negligible and the pump efficiency is 100%, the pump power, in kW, rounded off to 2 decimal places, is _____.

A metallic spherical particle of density 7001 kg/m³ and diameter 1 mm is settling steadily due to gravity in a stagnant gas of density 1 kg/m³ and viscosity \( 10^{-5} \) kg/(m·s). Take \( g = 9.8 \) m/s². Assume that the settling occurs in the regime where the drag coefficient \( C_D \) is independent of the Reynolds number and equals 0.44. The terminal settling velocity of the particle, in m/s, rounded off to 2 decimal places, is _____.

A Venturi meter with a throat diameter \( d = 2 \) cm measures the flow rate in a pipe of diameter \( D = 6 \) cm, as shown in the figure. A U-tube manometer is connected to measure the pressure drop. Assume the discharge coefficient is independent of the Reynolds number and geometric ratios. If the volumetric flow rate through the pipe is doubled (\( Q_2 = 2Q_1 \)), the corresponding ratio of the manometer readings \( \frac{\Delta_{h2}}{\Delta_{h1}} \), rounded off to the nearest integer, is ____.

Sulfur dioxide (SO₂) gas diffuses through a stagnant air-film of thickness 2 mm at 1 bar and 30 °C. The diffusion coefficient of SO₂ in air is 1 × 10⁻⁵ m² s⁻¹. The SO₂ partial pressures at the opposite sides of the film are 0.15 bar and 0.05 bar. The universal gas constant is 8.314 J mol⁻¹ K⁻¹. Assuming ideal gas behavior, the steady-state flux of SO₂ in mol m⁻² s⁻¹ through the air-film is

Consider the steady, uni-directional, fully-developed, pressure-driven laminar flow of an incompressible Newtonian fluid through a circular pipe of inner radius 5.0 cm. The magnitude of shear stress at the inner wall of the pipe is 0.1 N m\(^{-2}\). At a radial distance of 1.0 cm from the pipe axis, the magnitude of the shear stress, in N m\(^{-2}\), rounded off to 3 decimal places, is ____.

Consider a steady, fully-developed, uni-directional laminar flow of an incompressible Newtonian fluid (viscosity \(\mu\)) between two infinitely long horizontal plates separated by a distance \(2H\) as shown in the figure. The flow is driven by the combined action of a pressure gradient and the motion of the bottom plate at \( y = -H \) in the negative \( x \) direction. Given that \(\Delta P/L = (P_1 - P_2)/L > 0\), where \(P_1\) and \(P_2\) are the pressures at two \(x\) locations separated by a distance \(L\). The bottom plate has a velocity of magnitude \(V\) with respect to the stationary top plate at \(y = H\). Which one of the following represents the \(x\)-component of the fluid velocity vector?

An infinitely long cylindrical water filament of radius \( R \) is surrounded by air. Assume water and air to be static. The pressure outside the filament is \( P_{out} \) and the pressure inside is \( P_{in} \). If \( \gamma \) is the surface tension of the water-air interface, then \( P_{in} - P_{out} \) is:

The velocity field in an incompressible flow is \( \mathbf{v} = axy\hat{i} + v_y\hat{j} + \beta\hat{k} \), where \( \hat{i} \), \( \hat{j} \), and \( \hat{k} \) are unit vectors in the \( (x, y, z) \) Cartesian coordinate system. Given that \( a \) and \( \beta \) are constants, and \( v_y = 0 \) at \( y = 0 \), the correct expression for \( v_y \) is:

A soil sample was consolidated at a cell pressure of 10 K Pa for 24 hours during a cu test. The cell pressure increases to 30. Now it results in a core water pressure increment of 1 K Pa. Soil failed when the agsist test gradually increased to 50 K Pa. Core water pressure at failure was recorded as 21 K Pa. What is the scamton core water pressure B?