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In turbomachinery, the slip factor is a measure of the fluid slip in the impeller of a compressor or a turbine, mostly a centrifugal machine. Fluid slip is ... more
The tip-speed ratio, λ, or TSR for wind turbines is the ratio between the tangential speed of the tip of a blade and the actual ... more
All wind turbines operate with a yaw error. In this case an extreme yaw error of 30 degrees is assumed. The flapwise blade root bending moment due to that ... more
Wafer bonds are commonly characterized by three important encapsulation parameters: bond strength, hermeticity of encapsulation and bonding induced stress. ... more
Wafer bonds are commonly characterized by three important encapsulation parameters: bond strength, hermeticity of encapsulation and bonding induced ... more
In engineering, deflection is the degree to which a structural element is displaced under a load.
The elastic deflection of a weightless cantilever
... more
In engineering, deflection is the degree to which a structural element is displaced under a load. It may refer to an angle or a distance.
The angle of
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A cantilever is a beam anchored at only one end. The beam carries the load to the support where it is forced against by a moment and shear stress. A ... more
The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume. The mathematical ... more
The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume. The mathematical ... more
A cone is an n-dimensional geometric shape that tapers smoothly from a base (usually flat and circular) to a point called the apex or vertex. It is the ... more
NPSH characterize the potential for cavitation. The suction head coefficient is a dimensionless measure of ... more
The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume. The mathematical ... more
The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume. The mathematical ... more
In ductile materials, a plastic zone develops at the tip of the crack. The plastic loading and unloading cycle near the crack tip leads to the dissipation ... more
Description
A cone is an n-dimensional geometric shape that tapers smoothly from a base (usually flat and circular) to a point called the apex or ... more
The Euler’s pump and turbine equations are most fundamental equations in the field of turbo-machinery. These equations govern the power, efficiencies and ... more
Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid ... more
Nose cone section of any vehicle or body meant to travel through a compressible fluid medium (such as a rocket or aircraft, missile or bullet) has several ... more
The wafer bond characterization is based on different methods and tests. Wafer bonds are commonly characterized by three important encapsulation ... more
Centrifugal pumps are a sub-class of dynamic axis-symmetric work-absorbing turbo-machinery.The rotational energy typically comes from an engine or electric ... more
Mechanical components – as transmission gear and bearings – generates a mechanical loss that reduces the power transferred from the motor shaft ... more
The blade root bending moment due to the wind turbine yaw operation. The yaw rate can be calculated for passive yaw, or is defined by the design for active ... more
Due to leakage of fluid between the back surface of the impeller hub plate and the casing, or through other pump components – there is a volumetric ... more
The shaft bending moment due to yaw depends on the blades of the rotor. In this case the rotor has 2 blades
... more
The first image shows how helicopters store large amounts of rotational kinetic energy in their blades. This energy must be put into the blades before takeoff and maintained until the end of the flight. The engines do not have enough power to simultaneously provide lift and put significant rotational energy into the blades.
The second image shows a helicopter from the Auckland Westpac Rescue Helicopter Service. Over 50,000 lives have been saved since its operations beginning in 1973. Here, a water rescue operation is shown. (credit: 111 Emergency, Flickr)
Strategy
Rotational and translational kinetic energies can be calculated from their definitions. The last part of the problem relates to the idea that energy can change form, in this case from rotational kinetic energy to gravitational potential energy.
Solution for (a)
We must convert the angular velocity to radians per second and calculate the moment of inertia before we can find Er . The angular velocity ω for 1 r.p.m is
and for 300 r.p.m
The moment of inertia of one blade will be that of a thin rod rotated about its end.
The total I is four times this moment of inertia, because there are four blades. Thus,
and so The rotational kinetic energy is
Solution for (b)
Translational kinetic energy is defined as
To compare kinetic energies, we take the ratio of translational kinetic energy to rotational kinetic energy. This ratio is
Solution for (c)
At the maximum height, all rotational kinetic energy will have been converted to gravitational energy. To find this height, we equate those two energies:
Discussion
The ratio of translational energy to rotational kinetic energy is only 0.380. This ratio tells us that most of the kinetic energy of the helicopter is in its spinning blades—something you probably would not suspect. The 53.7 m height to which the helicopter could be raised with the rotational kinetic energy is also impressive, again emphasizing the amount of rotational kinetic energy in the blades.
Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/
The Moment magnitude scale is used to measure the size of earthquakes in terms of the energy released.The magnitude is based on the seismic moment of the ... more
Torque, is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as ... more
In geometry, a deltoid, also known as a tricuspoid or Steiner curve, is a hypocycloid of three cusps. In other words, it is the roulette created by a point ... more
In geometry, a deltoid, also known as a tricuspoid or Steiner curve, is a hypocycloid of three cusps. In other words, it is the roulette created by a point ... more
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A typical small rescue helicopter, like the one in the Figure below, has four blades, each is 4.00 m long and has a mass of 50.0 kg. The blades can be approximated as thin rods that rotate about one end of an axis perpendicular to their length. The helicopter has a total loaded mass of 1000 kg. (a) Calculate the rotational kinetic energy in the blades when they rotate at 300 rpm. (b) Calculate the translational kinetic energy of the helicopter when it flies at 20.0 m/s, and compare it with the rotational energy in the blades. (c) To what height could the helicopter be raised if all of the rotational kinetic energy could be used to lift it?