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Tension to restrain a floating object

Archimedes’ principle states that “Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the ... more

Hydrostatic weighing

Hydrostatic weighing, also referred to as “underwater weighing,” “hydrostatic body composition analysis,” and ... more

Reynolds number (for motion of an object in a viscous fluid)

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

Worksheet 300

Calculate the Reynolds number N′R for a ball with a 7.40-cm diameter thrown at 40.0 m/s.

Strategy

We can use the Reynolds number equation calculate N’R , since all values in it are either given or can be found in tables of density and viscosity.

Solution

We first find the kinematic viscosity values:

Kinematic Viscosity

Substituting values into the equation for N’R yields:

Reynolds number

Discussion

This value is sufficiently high to imply a turbulent wake. Most large objects, such as airplanes and sailboats, create significant turbulence as they move. As noted before, the Bernoulli principle gives only qualitatively-correct results in such situations.

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/

Womersley Number

The Womersley number (α) is a dimensionless number in biofluid mechanics. It is a dimensionless expression of the pulsatile flow frequency in relation to ... more

Reynolds number

In fluid mechanics, the Reynolds number (Re) is a dimensionless quantity that is used to help predict similar flow patterns in different fluid flow ... more

Characteristic Length

In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a ... more

Reynolds number (for a flow in a tube)

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

Drag force on a rigid cylinder when velocity is perpendicular to its axis(Slender-body theory)

n fluid dynamics and electrostatics, slender-body theory is a methodology that can be used to take advantage of the slenderness of a body to obtain an ... more

Drag force on a rigid cylinder when velocity is parallel to its axis(Slender-body theory)

In fluid dynamics and electrostatics, slender-body theory is a methodology that can be used to take advantage of the slenderness of a body to obtain an ... more

Rayleigh number (for the mushy zone of a solidifying alloy)

In fluid mechanics, the Rayleigh number (Ra) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free convection or ... more

Hedstrom number

The Hedstrom number is a dimensionless quantity used in fluid mechanics.

... more

Hartmann Number

Hartmann number (Ha) is the ratio of electromagnetic force to the viscous force first introduced by Hartmann.

... more

Weight

In science and engineering, the weight of an object is usually taken to be the force on the object due to gravity.
In Newtonian physics the weight is ... more

Bagnold number

he Bagnold number (Ba) is the ratio of grain collision stresses to viscous fluid stresses in a granular flow with interstitial Newtonian fluid, first ... more

Rayleigh number (for geophysical applications)

In fluid mechanics, the Rayleigh number (Ra) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free convection or ... more

Rayleigh number (for geophysical applications - related to bottom heating of the mantle from the core)

In fluid mechanics, the Rayleigh number (Ra) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free convection or ... more

Terminal velocity (creeping flow conditions)

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

Bernoulli's principle

Bernoulli’s principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with an increase in dynamic ... more

Roshko number

In fluid mechanics, the Roshko number is a dimensionless number describing oscillating flow mechanisms.It is related to the Strouhal number and the ... more

Worksheet 296

(a) Calculate the buoyant force on 10,000 metric tons (1.00×10 7 kg) of solid steel completely submerged in water, and compare this with the steel’s weight.

(b) What is the maximum buoyant force that water could exert on this same steel if it were shaped into a boat that could displace 1.00×10 5 m 3 of water?

Strategy for (a)

To find the buoyant force, we must find the weight of water displaced. We can do this by using the densities of water and steel given in Table [insert table #] We note that, since the steel is completely submerged, its volume and the water’s volume are the same. Once we know the volume of water, we can find its mass and weight

First, we use the definition of density to find the steel’s volume, and then we substitute values for mass and density. This gives :

Density

Because the steel is completely submerged, this is also the volume of water displaced, Vw. We can now find the mass of water displaced from the relationship between its volume and density, both of which are known. This gives:

Density

By Archimedes’ principle, the weight of water displaced is m w g , so the buoyant force is:

Force (Newton's second law)

The steel’s weight is 9.80×10 7 N , which is much greater than the buoyant force, so the steel will remain submerged.

Strategy for (b)

Here we are given the maximum volume of water the steel boat can displace. The buoyant force is the weight of this volume of water.

The mass of water displaced is found from its relationship to density and volume, both of which are known. That is:

Density

The maximum buoyant force is the weight of this much water, or

Force (Newton's second law)

Discussion

The maximum buoyant force is ten times the weight of the steel, meaning the ship can carry a load nine times its own weight without sinking.

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/

Normal force for a sinking object settles on the solid floor

When a sinking in a fluid object settles on the solid floor, it experiences a normal force.

... more

Kinematic Viscosity

Viscosity is a property arising from collisions between neighboring particles in a fluid that are moving at different velocities. When the fluid is forced ... more

Drag coefficient for a spherical object in creeping flow

In fluid dynamics, the drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, ... more

Critical grain size (diameter)

Sediment transport is the movement of solid particles (sediment), typically due to a combination of gravity acting on the sediment, and/or the movement of ... more

Stokes's Law of Sound Attenuation

Stokes’s law of sound attenuation is a formula for the attenuation of sound in a Newtonian fluid, such as water or air, due to the fluid’s ... more

Bejan number (modified form)

The modified form of the Bejan number, riginally proposed by Bhattacharjee and Grosshandler for momentum processes, by replacing the dynamic viscosity ... more

Reynolds number - Flow in a pipe with mass flow rate

For flow in a pipe or tube, the Reynolds number is generally defined as presented here.

For shapes such as squares, rectangular or annular ducts ... more

Taylor Number

In fluid dynamics, the Taylor number (Ta) is a dimensionless quantity that characterizes the importance of centrifugal “forces” or so-called ... more

Boundary shear stress (for natural rivers)

Assuming a single, well-mixed, homogeneous fluid and a single acceleration due to gravity (both are good assumptions in natural rivers, and the second is a ... more

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