2 First-Order Differential Equations Exercises 2.1 1. y 2. y y x t x t 3. y 4. y y x x t 5. y 6. y x x 7. y 8. y x x 17 Exercises 2.1 9. y 10. y x x 11. y 12. y x x 13. y 14. y x x 15. Writing the differential equation in the form dy/dx = y(1 − y)(1 + y) we see that critical points are located at y = −1‚ y = 0‚ and y = 1. The phase portrait is shown below. -1
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automobiles with air and they cause: Drag (resistance to forward motion) Lift / down force (come into play during cornering and acceleration) Lateral forces (comes into play during cornering) Moments in roll‚ pitch and yaw As a result these factors have to be taken into consideration during automobile design. THEORY BEHIND AERODYNAMIC FORCES The sources of aerodynamic forces are Viscous forces Drag (form drag) The major among both of these is the form drag caused by pressure differences between
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aerodynamics‚ drag‚ shape‚ size‚ forces‚ and gravity. Drag is the force of flight that pushes an airplane opposite to the direction it is moving. The biggest types of drag are friction‚ when air rubs against the surface‚ and difference in air pressure. Think of a drag like swimming treading through the water you can’t move as fast as you can on land the reason for that being because the water is causing drag on your body. The planes shape‚ size‚ and speed also affect the amount of drag on an aircraft
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DRDO Science Spectrum‚ March 2009‚ pp. 4-11 DRDO SCIENCE SPECTRUM 2009 © 2009‚ DESIDOC Aircraft Performance Improvements-A Practical Approach S.K. Jebakumar Centre for Military Airworthiness and Certification‚ Marathalli Colony‚ Bangaluru- 560 037 ABSTRACT An aircraft is designed based on various wind tunnel testing‚ computational analysis‚ previous design experience etc. In most of the aircraft programs the design objective could not be met with the first prototype design itself. Before the
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from Newton’s first law of motion‚ the acceleration then becomes zero and the object falls at a constant terminal velocity. Ideally‚ a parachute will slow the object’s speed by creating air drag that eventually overpowers the force of gravity‚ causing the falling object to decelerate. However‚ since the air drag is dependent on the velocity‚ the air resistance
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A dragline excavator is a piece of heavy equipment used in civil engineering and surface mining. Draglines fall into two broad categories: those that are based on standard‚ lifting cranes and the heavy units which have to be built on-site. Most crawler cranes with an added winch drum on the front can act as a dragline. These units (like other cranes) are designed to be dismantled and transported over the road on flatbed trailers. Draglines used in civil engineering are almost always of this smaller
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of flow layer . . . . . . . . . . . . . . . . . . . . . . . . . . . Velocity distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 4 5 7 9 Ch´zy coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 e Drag coefficient‚ lift coefficient and friction coefficient . . . . . . . . . . . . 14 Exercise .
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EFFECT OF SURFACE AREA ON AIR FRICTION Design Background Information: Air resistance‚ also called drag‚ is the forces that are in opposition to the relative motion of an object through the air. Drag forces act opposite to the oncoming flow velocity. Size and shape are the two factors that affect air resistance. Air resistance depends on the surface area‚ so‚ as the surface area increases‚ the air resistance increases. When an object is falling‚ air resistance acts to push it back up. This is
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MAT114 Multivariable Calculus and Differential Equations Version No. 1.00 Course Prerequisites L T P C 3 0 2 4 : 10+2 level Mathematics/ Basic Mathematics (MAT001) Objectives This Mathematics course provides requisite and relevant background necessary to understand the other important engineering mathematics courses offered for Engineers and Scientists. Three important topics of applied mathematics‚ namely the Multiple integrals‚ Vector calculus‚ Laplace transforms which require knowledge of
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the branch of science concerning the study of matter and energy and the interactions between the two. Physics tries to explain the nature of the world around us‚ how things happen and why. Swimming displays some physical properties‚ such as buoyancy‚ drag resistance and propulsion. We swimmers are at a constant battle to stay afloat‚ while fighting through the water and propelling ourselves forward‚ and we do so using technique. Buoyancy is the power to float or rise in a fluid. This relates to swimming
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