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Cryoscopic constant

Freezing-point depression describes the process in which adding a solute to a solvent decreases the freezing point of the solvent. freezing-point ... more

Boiling point elevation (ebullioscopy)

Colligative properties are properties of solutions that depend upon the ratio of the number of solute particles to the number of solvent molecules in a ... more

Ebullioscopic constant

An ebullioscope (from the Latin ēbullīre is an instrument for measuring the boiling point of a liquid. This can be used for determining the alcoholic ... more

Osmotic pressure (Morse equation)

Osmotic pressure is the pressure which needs to be applied to a solution to prevent the inward flow of water across a semipermeable membrane. The osmotic ... more

Molality

In chemistry, the molality of a solution is defined as the amount of substance of solute,, divided by the mass of the solvent, (not the mass of the ... more

Henry's law

In physics, Henry’s law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. ... more

Osmotic pressure

is the minimum pressure which needs to be applied to a solution to prevent the inward flow of water across a semipermeable membrane. It is also defined as ... more

Floating objects (weight that depresses the surface)

When an object is placed on a liquid, its weight depresses the surface, and is balanced by the surface tension forces on either side , which are each ... more

Peng–Robinson equation of state

The Peng–Robinson equation of state (PR EOS) was developed in 1976 at The University of Alberta by Ding-Yu Peng and Donald ... more

Diffusion coefficient (Mass diffusivity) for liquids

Diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration ... more

Dilution

Dilution is a reduction in the concentration of a chemical (gas, vapor, solution). It is the process of reducing the concentration of a solute in solution, ... more

Darcy friction factor - Serghides's solution

In fluid dynamics, the Darcy friction factor formulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used ... more

Water flux (Forward osmosis application)

Forward osmosis (FO) is an osmotic process that, like reverse osmosis (RO), uses a semi-permeable membrane to effect separation of water from dissolved ... more

Solute flux (Forward osmosis)

Forward osmosis (FO) is an osmotic process that, like reverse osmosis (RO), uses a semi-permeable membrane to effect separation of water from dissolved ... more

Worksheet 333

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?


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

Angular velocity

and for 300 r.p.m

Multiplication

The moment of inertia of one blade will be that of a thin rod rotated about its end.

Moment of Inertia - Rod end

The total I is four times this moment of inertia, because there are four blades. Thus,

Multiplication

and so The rotational kinetic energy is

Rotational energy

Solution for (b)

Translational kinetic energy is defined as

Kinetic energy ( related to the object 's velocity )

To compare kinetic energies, we take the ratio of translational kinetic energy to rotational kinetic energy. This ratio is

Division

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:

Potential energy

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/

Darcy friction factor - Serghides's solution (Variable B)

In fluid dynamics, the Darcy friction factor formulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used ... more

Darcy friction factor - Serghides's solution (Variable C)

In fluid dynamics, the Darcy friction factor formulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used ... more

Pell's equation

Pell’s equation is a Diophantine equation (a polynomial equation in two or more unknowns ).
In Cartesian coordinates, the equation has the form ... more

Danish-Kumar Solution (for Buckingham-Reiner equation)

A Bingham plastic is a viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress. It is named after ... more

Darcy friction factor - Brkić solution

In fluid dynamics, the Darcy friction factor formulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used ... more

Monatomic ideal gas heat capacity at constant volume

Heat capacity or thermal capacity is a physical quantity equal to the ratio of the heat that is added to (or removed from) an object to the resulting ... more

Monatomic ideal gas heat capacity at constant pressure

Heat capacity or thermal capacity is a physical quantity equal to the ratio of the heat that is added to (or removed from) an object to the resulting ... more

Darcy friction factor - Serghides's solution (Variable A)

In fluid dynamics, the Darcy friction factor formulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used ... more

Darcy friction factor - Brkić solution (Variable S)

In fluid dynamics, the Darcy friction factor formulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used ... more

Diffusion coefficient (Mass diffusivity) for gases

Diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration ... more

Solute sieving coefficient

The selection of synthetic membranes for a targeted separation process is usually based on few requirements. Membranes have to provide enough mass transfer ... more

Speed of Sound (air, ideal gases) - relative to molar mass

The speed of sound is the distance travelled per unit time by a sound wave propagating through an elastic medium. The SI unit of the speed of sound is the ... more

Van 't Hoff equation

The Van 't Hoff equation in chemical thermodynamics relates the change in the equilibrium constant, Keq, of a chemical equilibrium to the change in ... more

Daniell cell

The Daniell cell is a type of electrochemical cell consisted of a copper pot filled with a copper sulfate solution, in which was immersed an unglazed ... more

K2 for Danish-Kumar Solution

A Bingham plastic is a viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress. It is named after ... more

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