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Prandtl–Meyer expansion fan - Prandtl–Meyer function

A supersonic expansion fan, technically known as Prandtl–Meyer expansion fan, is a centred expansion process that occurs when a supersonic flow turns ... more

Knudsen diffusivity for diffusing species

Knudsen diffusion is a means of diffusion that occurs when the scale length of a system is comparable to or smaller than the mean free path of the ... more

Maxwell–Boltzmann statistics

In statistical mechanics, Maxwell–Boltzmann statistics describes the average distribution of non-interacting material particles over various energy states ... more

Shock Diamond - distance from the nozzle

Shock diamonds (also known as Mach diamonds, Mach disks, Mach rings, doughnut tails or thrust diamonds) are a formation of standing wave patterns that ... more

Prandtl–Meyer expansion fan - turn angle

A supersonic expansion fan, technically known as Prandtl–Meyer expansion fan, is a centred expansion process that occurs when a supersonic flow turns ... more

Prandtl–Meyer expansion fan - Maximum turn angle

A supersonic expansion fan, technically known as Prandtl–Meyer expansion fan, is a centred expansion process that occurs when a supersonic flow turns ... 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
Prandtl–Meyer expansion fan - final flow tempreture

A supersonic expansion fan, technically known as Prandtl–Meyer expansion fan, is a centred expansion process that occurs when a supersonic flow turns ... more

Prandtl–Meyer expansion fan - final flow pressure

A supersonic expansion fan, technically known as Prandtl–Meyer expansion fan, is a centred expansion process that occurs when a supersonic flow turns ... more

Oblique Shock

An oblique shock wave, unlike a normal shock, is inclined with respect to the incident upstream flow direction. It will occur when a supersonic flow ... more

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