Boundary Layer Theory Drag And Lift Practice Questions

Two discrete spherical particles (P and Q) of equal mass density are independently released in water. Particle P and particle Q have diameters of 0.5 mm and 1.0 mm, respectively. Assume Stokes' law is valid. The drag force on particle Q will be________ times the drag force on particle P. (round off to the nearest integer)

Velocity distribution in a boundary layer is given by $\frac{u}{U_\infty }=\sin \left ( \frac{\pi}{2}\frac{y}{\delta } \right )$ , where $u$ is the velocity at vertical coordinate $y, U_\infty$ is the free stream velocity and $\delta$ is the boundary layer thickness. The values of $U_\infty$ and $\delta$ are 0.3 m/s and 1.0 m, respectively. The velocity gradient $\left ( \frac{\partial u}{\partial y} \right )$ (in $s^{-1}$ , round off to two decimal places) at y= 0, is ________.

Consider a laminar flow in the x-direction between two infinite parallel plates (Couette flow). The lower plate is stationary and the upper plate is moving with a velocity of 1 cm/s in the x-direction. The distance between the plates is 5 mm and the dynamic viscosity of the fluid is 0.01 $N-s/m^2$ . If the shear stress on the lower plate is zero, the pressure gradient, $\frac{\partial p}{\partial x}$ , (in $N/m^2$ per m,round off to 1 decimal place)is _______

An automobile with projected area 2.6 $m^{2}$ is running on a road with a speed of 120 km per hour. The mass density and the kinematic viscosity of air are 1.2 $kg/m^{3}$ and $1.5 \times 10^{-5} m^{2}/s$ , respectively. The drag coefficient is 0.30. The metric horse power required to overcome the drag force is

The thickness of the laminar boundary layer on a flat plate at a point A is 2 cm and at a point B, 1 m downstream of A, is 3 cm. What is the distance of A from the leading edge of the plate ?

An aircraft is flying in level flight at a speed of 200 km/hr through air (density, $\rho =1.2 kg/m^{3}$ , and viscosity $\mu =1.6 \times 10^{-5} Ns/m^{2}$ ). The lift coefficient at this speed is 0.4 and the drag coefficient is 0.0065. The mass of the aircraft is 800 kg. The effective lift area of the aircraft is

A thin flat plate $0.5m\times 0.7m$ in size settles in a large tank of water with a terminal velocity of 0.12 m/s. The coefficients of drag $C_{D}=\frac{1.328}{\sqrt{R_{L}}}$ for a laminar boundary layer and $C_{D}=\frac{0.072}{(R_{L})^{1/5}}$ for a turbulent boundary layer, where $R_L$ is the plate Reynolds number. Assume $\mu=10^{-3} N-s/m^{2}$ and $\rho =1000 kg/m^{3}$ The submerged weight of the plate is

A solid sphere (diameter 6 mm) is rising through oil (mass density 900 $kg/m^{3}$ , dynamic viscosity 0.7 kg/ms) at a constant velocity of 1 cm/s. What is the specific weight of the material form which the sphere is made ? (Take g = 9.81 $m/s^{2}$ )

A flat plate is kept in an infinite fluid medium. The fluid has a uniform free-stream velocity parallel to the plate. For the laminar boundary layer formed on the plate, pick the correct option matching Columns I and II.

Velocity distribution in a boundary layer flow over a plate is given by $(u/u_{m})=1.5 \eta$ where, $\eta =y/\delta$ ; y is the distance measured normal to the plate; $\delta$ is the boundary layer thickness; and $u_m$ is the maximum velocity at $y =\delta$ . If the shear stress $\tau$ , acting on the plate is given by $\tau =K(\mu u_{m})\delta$ where, $\mu$ is the dynamic viscosity of the fluid, K takes the value of