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Law of the wall

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

Superformula - Polar Equation

The superformula is a generalization of the superellipse and was first proposed by Johan Gielis in 2003. Gielis suggested that the formula can be used to ... more

Area Moment of Inertia - Filled Right Triangle

The second moment of area, also known as moment of inertia of plane area, area moment of inertia, polar moment of area or second area moment, is a ... more

Superformula - Parametric Equation for X Axis

The superformula is a generalization of the superellipse and was first proposed by Johan Gielis in 2003. Gielis suggested that the formula can be used to ... more

Superformula - Parametric Equation for Y Axis

The superformula is a generalization of the superellipse and was first proposed by Johan Gielis in 2003. Gielis suggested that the formula can be used to ... more

Right Triangle (sides)

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree ... 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
Kepler's equation - X coordinate

In orbital mechanics, Kepler’s equation relates various geometric properties of the orbit of a body subject to a central force.

It was first ... more

Curved Area of a Hemisphere

A sphere is a perfectly round geometrical and circular object in three-dimensional space that resembles the shape of a completely round ball. A sphere is ... more

Brinell Hardness Number

BHN or Brinell Number is the numerical value assigned to the hardness of metals and alloys. The test is to determine the hardness ... more

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