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Bernoulli’s equation states that for an incompressible, frictionless fluid, the above mentioned sum is constant. If we follow a small volume of fluid along ... more

Vertical pressure variation is the variation in pressure as a function of elevation. The vertical variation is especially significant, as it results from ... more

In a hydraulic circuit, net positive suction head (NPSH) may refer to one of two quantities in the analysis of cavitation:

... more

The gravity of Earth, which is denoted by g, refers to the acceleration that the Earth imparts to objects on or near its surface due to gravity. In SI ... more

Borda–Carnot equation is an empirical description of the mechanical energy losses of the fluid due to a (sudden) flow expansion. It describes how the total ... more

Drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) refers to forces acting ... more

The terminal velocity of a falling object is the velocity of the object when the sum of the drag force and buoyancy equals the downward force of gravity ... more

The Sherwood number (Sh) is a dimensionless number used in mass-transfer operation. It can be further defined as a function of the Reynolds and Schmidt ... more

In a fluid at rest, all frictional stresses vanish and the state of stress of the system is called hydrostatic.For water and other liquids, this integral ... more

Thrust is a reaction force described quantitatively by Newton’s second and third laws. When a system expels or accelerates mass in one direction, the ... more

Potential energy is the energy of a body or a system with respect to the position of the body or the arrangement of the particles of the system. The amount ... more

The depth–slope product is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow. The ... more

The terminal velocity of a falling object is the velocity of the object when the sum of the drag force and buoyancy equals the downward force of gravity ... more

Drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) refers to forces acting ... more

where **Vt** is the terminal velocity,
**m** is the mass of the skydiver,
**g** is the acceleration due to gravity,
**C _{d}** is the drag coefficient,

**ρ**is the density of the fluid through which the object is falling, and

**A**is the projected area of the object.

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/

where h is skydiver height and w the width at “spread-eagle” position

In fluid mechanics, the Reynolds number is used to help predict if flow will be laminar or turbulent. We know that the flow around a smooth, streamlined ... 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 Newtonian fluid is a fluid in which the viscous stresses arising from its flow, at every point, are proportional to the local strain rate — the rate of ... more

In fluid mechanics, the Reynolds number is used to help predict if flow will be laminar or turbulent. We know that flow in a very smooth tube, streamlined ... more

In fluid dynamics, the law of the wall states that the average velocity of a turbulent flow at a certain point is proportional to the logarithm of the ... more

In fluid dynamics the Borda–Carnot equation is an empirical description of the mechanical energy losses of the fluid due to a (sudden) flow expansion. The ... more

The weight of an object is the force on the object due to gravity. Buoyancy is an upward force exerted by a fluid that opposes the weight of an immersed ... more

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 **E _{r}** . 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/

In aerodynamics, wing loading is the total weight of an aircraft divided by the area of its wing. The stalling speed of an aircraft in straight, level ... more

In fluid flow, friction loss (or skin friction) is the loss of pressure or “head” that occurs in pipe or duct flow due to the effect of the fluid’s ... more

The elliptic paraboloid is shaped like an oval cup and can have a maximum or minimum point. In a suitable coordinate system with three axes x, y, and z, it ... more

In viscous fluid dynamics, the Archimedes number (Ar) (not to be confused with Archimedes’ constant, π), named after the ancient Greek scientist ... more

In astrodynamics, the vis viva equation, also referred to as orbital energy conservation equation, is one of the fundamental equations that govern the ... more

Borda–Carnot equation is an empirical description of the mechanical energy losses of the fluid due to a (sudden) flow expansion. It describes how the total ... more

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Find the terminal velocity of an

85-kgskydiver falling in a spread-eagle position.