Fluid Mechanics Flashcards

Question

FRICTION AND PRESSURE DRAG Reducing Drag by Streamlining Flow Separation DRAG COEFFICIENTS OF COMMON GEOMETRIES PARALLEL FLOW OVER FLAT PLATES FLOW OVER CYLINDERS AND SPHERES

Answer 1

FRICTION AND PRESSURE DRAG part of drag that is due directly to wall shear stress is called the skin friction drag (or just friction drag) since it is caused by frictional effects, and the part that is due directly to pressure P is called the pressure drag (also called the form drag because of its strong dependence on the form or shape of the body) friction drag is the component of the wall shear force in the direction of flow, and thus it depends on the orientation of the body as well as the magnitude of the wall shear stress. Friction drag is a strong function of viscosity, and increases with increasing viscosity. The friction drag is also proportional to the surface area. The friction drag coefficient is independent of surface roughness in laminar flow, but is a strong function of surface roughness in turbulent flow due to surface roughness elements protruding further into the boundary layer. The friction drag coefficient is analogous to the friction factor in pipe flow, and its value depends on the flow regime. The pressure drag is proportional to the frontal area and to the difference between the pressures acting on the front and back of the immersed body. The pressure drag becomes most significant when the velocity of the fluid is too high for the fluid to be able to follow the curvature of the body, and thus the fluid separates from the body at some point and creates a very low pressure region in the back. The pressure drag in this case is due to the large pressure difference between the front and back sides of the body. Reducing Drag by Streamlining streamlining has opposite effects on pressure and friction drags. It decreases pressure drag by delaying boundary layer separation and thus reducing the pressure difference between the front and back of the body and increases the friction drag by increasing the surface area. The end result depends on which effect dominates. Therefore, any optimization study to reduce the drag of a body must consider both effects and must attempt to minimize the sum of the two. Streamlining has the added benefit of reducing vibration and noise. Streamlining should be considered only for blunt bodies that are subjected to high-velocity fluid flow (and thus high Reynolds numbers) for which flow separation is a real possibility. It is not necessary for bodies that typically involve low Reynolds number flows (e.g., creeping flows in which Re Ͻ 1), since the drag in those cases is almost entirely due to friction drag, and streamlining will only increase the surface area and thus the total drag Flow Separation At sufficiently high velocities, the fluid stream detaches itself from the surface of the body. This is called flow separation. The region of flow trailing the body where the effects of the body on velocity are felt is called the wake. The separated region comes to an end when the two flow streams reattach. Therefore, the separated region is an enclosed volume, whereas the wake keeps growing behind the body until the fluid in the wake region regains its velocity and the velocity profile becomes nearly flat again. Viscous and rotational effects are the most significant in the boundary layer, the separated region, and the wake. Flow separation on the top surface of a wing reduces lift drastically and may cause the airplane to stall. drag and lift are strongly dependent on the shape of the body, and any effect that causes the shape to change has a profound effect on the drag and lift. important consequence of flow separation is the formation and shedding of circulating fluid chunks, called vortices, in the wake region. The periodic generation of these vortices downstream is referred to as vortex shedding. DRAG COEFFICIENTS OF COMMON GEOMETRIES The drag coefficients for most geometries (but not all) remain essentially constant at Reynolds numbers above about 10^4 . This is due to the flow at high Reynolds numbers becoming fully turbulent. However, this is not the case for rounded bodies such as circular cylinders and spheres. at low Reynolds numbers, the shape of the body does not have a major influence on the drag coefficient the drag coefficient at high Reynolds numbers. First of all, the orientation of the body relative to the direction of flow has a major influence on the drag coefficient. As a rule of thumb, the percentage of fuel savings due to reduced drag is about half the percentage of drag reduction. the ideal shape of a vehicle is the basic teardrop, with a drag coefficient of about 0.1 for the turbulent flow case PARALLEL FLOW OVER FLAT PLATES FLOW OVER CYLINDERS AND SPHERES A sudden drop in the drag coefficient somewhere in the range of 10^5 < Re < 10^6. This large reduction in C D is due to the flow in the boundary layer becoming turbulent, which moves the separation point further on the rear of the body, reducing the size of the wake and thus the magnitude of the pressure drag. This is in contrast to streamlined bodies, which experience an increase in the drag coefficient (mostly due to friction drag) when the boundary layer becomes turbulent. The delay of separation in turbulent flow is caused by the rapid fluctuations of the fluid in the transverse direction, which enables the turbulent boundary layer to travel farther along the surface before separation occurs, resulting in a narrower wake and a smaller pressure drag. In the range of Reynolds numbers where the flow changes from laminar to turbulent, even the drag force F D decreases as the velocity (and thus the Reynolds number) increases. This results in a sudden decrease in drag of a flying body (sometimes called the drag crisis) and instabilities in flight. surface roughness, in general, increases the drag coefficient in turbulent flow. This is especially the case for streamlined bodies. For blunt bodies such as a circular cylinder or sphere, however, an increase in the surface roughness may actually decrease the drag coefficient. roughening the surface can be used to great advantage in reducing drag, but it can also backfire on us if we are not careful—specifically, if we do not operate in the right range of the Reynolds number. golf balls are intentionally roughened to induce turbulence at a lower Reynolds number to take advantage of the sharp drop in the drag coefficient at the onset of turbulence in the boundary layer. The occurrence of turbulent flow reduces the drag coefficient of a golf ball by about half. Tennis balls travel short distances and never reach turbulent range.

Answer 2

LIFT airfoils are specifically designed to generate lift while keeping the drag at a minimum. some devices such as the spoilers and inverted airfoils on racing cars are designed for the opposite purpose of avoiding lift or even generating negative lift to improve traction and control. lift in practice can be taken to be due entirely to the pressure distribution on the surfaces of the body, and thus the shape of the body has the primary influence on lift. Then the primary consideration in the design of airfoils is minimizing the average pressure at the upper surface while maximizing it at the lower surface. lift is practically independent of the surface roughness since roughness affects the wall shear, not the pressure. the contribution of viscous effects to lift is negligible, we should be able to determine the lift acting on an airfoil by simply integrating the pressure distribution around the airfoil. The pressure changes in the flow direction along the surface, but it remains essentially constant through the boundary layer in a direction normal to the surface. Therefore, it seems reasonable to ignore the very thin boundary layer on the airfoil and calculate the pressure distribution around the airfoil from the relatively simple potential flow theory (zero vorticity, irrotational flow) for which net viscous forces are zero for flow past an airfoil. At zero angle of attack, the lift produced by the symmetrical airfoil is zero, as expected because of symmetry, and the stagnation points are at the leading and trailing edges. For the nonsymmetrical airfoil, which is at a small angle of attack, the front stagnation point has moved down below the leading edge, and the rear stagnation point has moved up to the upper surface close to the trailing edge. To our surprise, the lift produced is calculated again to be zero—a clear contradiction of experimental observations and measurements. Obviously, the theory needs to be modified to bring it in line with the observed phenomenon. the two flow streams from the top and the bottom sides of the airfoil meet at the trailing edge, yielding a smooth flow downstream parallel to the trailing edge. Lift is generated because the flow velocity at the top surface is higher, and thus the pressure on that surface is lower due to the Bernoulli effect. after a sudden increase in angle of attack, a counterclockwise starting vortex is shed from the airfoil, while clockwise circulation appears around the airfoil, causing lift to be generated. It is desirable for airfoils to generate the most lift while producing the least drag. The flaps are used to alter the shape of the wings during takeoff and landing to maximize lift and to enable the aircraft to land or take off at low speeds. Tip vortices that interact with the free stream impose forces on the wing tips in all directions, including the flow direction. The component of the force in the flow direction adds to drag and is called induced drag. end effects can be minimized by attaching endplates or winglets at the tips of the wings perpendicular to the top surface. The endplates function by blocking some of the leakage around the wing tips, which results in a considerable reduction in the strength of the tip vortices and the induced drag. large commercial planes (and soaring birds like albatrosses) have long and narrow wings - bodies with large aspect ratios fly more efficiently, but they are less maneuverable because of their larger moment of inertia fighter planes (and fighter birds like falcons) have short and wide wings - manoeuvre better since the wings are closer to the central part The lift coefficient increases almost linearly with the angle of attack a reaches a maximum at about angle16° and then starts to decrease sharply. This decrease of lift with further increase in the angle of attack is called stall, and it is caused by flow separation and the formation of a wide wake region over the top surface of the airfoil. Stall is highly undesirable since it also increases drag. At zero angle of attack (0°), the lift coefficient is zero for symmetrical airfoils but nonzero for nonsymmetrical ones with greater curvature at the top surface.

Answer 3

Drag - Skin friction - shear stresses (surface) Pressure Drag - difference in front & back pressure (shape) Interference drag - mixing of airflow streamlines between airframe components such as wing & fuselage Induced drag - due to wingtip vortices (winglets/ endplates are used to prevent wingtip vortices) upwash - birds & fighter planes fly in V formation to take advantage of upwash which helps in supporting weight. Lift Generated by Spinning The phenomenon of producing lift by the rotation of a solid body is called the Magnus effect. The stagnation points shift down, and the flow is no longer symmetric about the horizontal plane that passes through the center of the cylinder. The average pressure on the upper half is less than the average pressure at the lower half because of the Bernoulli effect, and thus there is a net upward force (lift) acting on the cylinder.

Answer 4

Ch. 12 Compressible Flows STAGNATION PROPERTIES Enthalpy - Internal Energy + Flow Energy Stagnation Enthalpy or Total Enthalpy - Enthalpy + Kinetic Energy when potential energy is negligible - total enthalpy represents the total energy of flowing fluid stream. static enthalpy - ordinary enthalpy stagnation enthalpy - enthalpy of a fluid when it is brought to rest adiabatically Isentropic stagnation enthalpy - when the stagnation process is reversible & adiabatic. Dynamic Temperature - V2/(2Cp) SPEED OF SOUND AND MACH NUMBER Speed of Sound - the speed at which an infinitesimally small pressure wave travels through a medium (c=sqrt(gammaRT)) Ma - ratio of velocity of object to the velocity of sound in that medium, Ma = V/c Subsonic < 1 , Supersonic > 1 , Hypersonic >> 1 , Transonic around 1 ONE-DIMENSIONAL ISENTROPIC FLOW Supersonic flow continues accelerating even when the section is diverging because mass flow is constant large decrease in density makes acceleration in the diverging section possible. ISENTROPIC FLOW THROUGH NOZZLES Converging Nozzles the effects of back pressure (i.e., the pressure applied at the nozzle discharge region) on the exit velocity, the mass flow rate, and the pressure distribution along the nozzle. Converging–Diverging Nozzles

Answer 5

SHOCK WAVES AND EXPANSION WAVES Shock waves - abrupt changes in fluid properties occuring in a very thin section of fluid flow. Normal shock waves - shock waves that occur in a plane normal to the direction of flow are called normal shock waves. Flow across the shock wave is highly irreversible & can't be approximated as isentropic. Decrease - V, Ma, Po Increase - P, T, To S, rho Fanno line - locus of states that have same stagnation enthalpy & mass flow rate on h-s diagram. Rayleigh line - locus of states that have same momentum & mass on h-s diagram. Oblique Shocks - produced in compressing flows Prandtl-Meyer Expansion Waves - Expanding Flows produces Expansion waves (not shock waves). Flow doesn't turn suddenly but gradually & the flow region is isentropic in expanding region. Composed of infinite number of Mach waves called Prandtl-Meyer expansion waves.

Answer 6

DUCT FLOW WITH HEAT TRANSFER AND NEGLIGIBLE FRICTION (RAYLEIGH FLOW) Plot of Rayleigh flow on a T-s diagram is called the Rayleigh line. The states on the upper arm of the Rayleigh line above point a are subsonic, and the states on the lower arm below point a are supersonic. Therefore, a process proceeds to the right on the Rayleigh line with heat addition and to the left with heat rejection regardless of the initial value of the Mach number. Heating increases the Mach number for subsonic flow, but decreases it for supersonic flow. The flow Mach number approaches Ma=1 in both cases (from 0 in subsonic flow and from infinity in supersonic flow) during heating. Table that shows the effects of heating & cooling on the properties of Rayleigh flow for subsonic & supersonic case.

Answer 7

ADIABATIC DUCT FLOW WITH FRICTION (FANNO FLOW) Plot of Fanno flow on T-s diagram is called Fanno line. Friction causes entropy to increase, and thus a process always proceeds to the right along the Fanno line. At the point of maximum entropy, the Mach number is Ma=1. All states on the upper part of the Fanno line are subsonic, and all states on the lower part are supersonic. Friction increases the Mach number for subsonic Fanno flow, but decreases it for supersonic Fanno flow. The Mach number approaches unity (Ma=1) in both cases. The energy balance requires that stagnation temperature T_o=T+V^2/2C_p remain constant during Fanno flow. But the actual temperature may change. Velocity increases and thus temperature decreases during subsonic flow, but the opposite occurs during supersonic flow. Table that shows the effects of friction on properties of Fanno flow, for subsonic & supersonic.

Answer 8

Flows in circular paths are called vortex flows, some basic forms of which are described in what follows. Solid-Body Rotation circular cylinder rotating with constant angular velocity Irrotational Vortex ur = constant Rankine Vortex Real vortices, such as a bathtub vortex or an atmospheric cyclone, have a core that rotates nearly like a solid body and an approximately irrotational far field An idealization of such a behavior is called the Rankine vortex, in which the vorticity is assumed uniform within a core of radius R and zero outside the core