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Dupuit-Forchheimer relationship

The pore or interstitial velocity v_px given by the Dupuit-Forchheimer relationship is the average velocity of fluid molecules in the pores; it is related ... more

Density

The density of a material is defined as its mass per unit volume. For a pure substance the density has the same numerical value as its mass concentration. ... more

Normalized water content ( effective saturation van Genuchten)

In soil mechanics and petroleum engineering, water content or soil moisture content is the quantity of water contained in the soil. The normalized water ... more

Submerged unit weight

In fluid mechanics, specific weight ( or unit weight ) represents the force exerted by gravity on a unit volume of a fluid. Specific weight can be used as ... 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/

Volumetric water content

Water content or moisture content is the quantity of water contained in a material, such as soil (called soil moisture), rock, ceramics, fruit, or wood. ... more

Relative density of soil

Silts, sands and gravels are classified by their size, and hence they may consist of a variety of minerals. Owing to the stability of quartz compared to ... more

Time to reach specific temperature (related to Biot and Fourier numbers)

The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations. Gives a simple index of the ratio of the heat transfer resistances ... more

Hydraulic conductivity (Falling-head method)

Hydraulic conductivity is a property of vascular plants, soils and rocks, that describes the ease with which a fluid (usually water) can move through pore ... more

Bulk Modulus - volume

The bulk modulus ( or ) of a substance measures the substance’s resistance to uniform compression. It is defined as the ratio of the infinitesimal ... more

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