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Ultrasonic flow meter ( speed of sound )

An ultrasonic flow meter is a type of flow meter that measures the velocity of a fluid with ultrasound to calculate volume flow. Ultrasonic flow meters are ... more

Benford's Law

Benford’s Law, also called the First-Digit Law, refers to the frequency distribution of digits in many (but not all) real-life sources of data. In ... more

Future value of a present sum

A time value of money calculation is one which solves for one of several variables in a financial problem. In a typical case, the variables might be: a ... more

Volume of a tetrahedron

A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. It has six edges and four ... more

Hooke's law for continuous media

Hooke’s law states that the force needed to extend or compress a spring by some distance is proportional to that distance.The stresses and strains ... 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
Fin Area on a Rocket

The size of the fins controls a rocket’s stability and the amount of weather cocking (turning into the wind). The best way to determine final fin ... more

Compartmental SIR model in epidemiology (basic reproduction number)

In order to model the progress of an epidemic in a large population, the population diversity must be reduced to a few key characteristics which are ... more

Bayes' theorem

In probability theory, a conditional probability measures the probability of an event given that (by assumption, presumption, assertion or evidence) ... more

Inclusive Graphic Standard Deviation

Is the measure of sorting or variation of a particle size distribution in phi scale; can be estimated from the percentages of the particles which ... more

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