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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

Worksheet 341

The awe‐inspiring Great Pyramid of Cheops was built more than 4500 years ago. Its square base, originally 230 m on a side, covered 13.1 acres, and it was 146 m high (H), with a mass of about 7×10^9 kg. (The pyramid’s dimensions are slightly different today due to quarrying and some sagging). Historians estimate that 20,000 workers spent 20 years to construct it, working 12-hour days, 330 days per year.

a) Calculate the gravitational potential energy stored in the pyramid, given its center of mass is at one-fourth its height.

Division
Potential energy

b) Only a fraction of the workers lifted blocks; most were involved in support services such as building ramps, bringing food and water, and hauling blocks to the site. Calculate the efficiency of the workers who did the lifting, assuming there were 1000 of them and they consumed food energy at the rate of 300 Kcal/hour.

first we calculate the number of hours worked per year.

Multiplication

then we calculate the number of hours worked in the 20 years.

Multiplication

Then we calculate the energy consumed in 20 years knowing the energy consumed per hour and the total hours worked in 20 years.

Multiplication
Multiplication

The efficiency is the resulting potential energy divided by the consumed energy.

Division
Heronian mean

The Heronian mean of two non-negative real numbers is a weighted mean of their arithmetic and geometric means.The weighted mean is similar to an ... more

Final Grade conversion to the German system - Bavarian Formular

A number of systems exist for the conversion of grades from other countries into German grades. One such system, used by most universities in ... more

Head loss in terms of volumetric flow rate

Hydraulic head or piezometric head is a specific measurement of liquid pressure above a geodetic datum.
In any real moving fluid, energy is dissipated ... more

Preload (cardiac)

Preload is described as the stretching of a single cardiac myocyte immediately prior to contraction and is, therefore, related to the sarcomere length. ... more

Bose–Einstein statistics ( εi > μ)

In quantum statistics, Bose–Einstein statistics (or more colloquially B–E statistics) is one of two possible ways in which a collection of non-interacting ... more

Capital asset pricing model ( including size premium and specific risk)

In finance, the capital asset pricing model (CAPM) is used to determine a theoretically appropriate required rate of return of an ... more

Weighted power mean

The weighted mean is similar to an arithmetic mean (the most common type of average), where instead of each of the data points contributing equally to the ... more

Machinability Index

The term machinability refers to the ease with which a metal can be cut (machined) permitting the removal of the material with a satisfactory finish at low ... more

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