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Volume thermal expansion coefficient

Thermal expansion is the tendency of matter to change in volume in response to a change in temperature through heat transfer. For a solid, we can ignore ... 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
Speed of Sound in Solids - long rods

The speed of sound is the distance travelled per unit of time by a sound wave propagating through an elastic medium.
The speed of sound for ... more

Speed of Sound in Fluids (Newton-Laplace equation )

The speed of sound is the distance travelled per unit of time by a sound wave propagating through an elastic medium.
Sound travels faster in liquids ... more

Friction Loss (hydraulic slope)

In fluid flow, friction loss (or skin friction) is the loss of pressure or “head” that occurs in pipe or duct flow due to the effect of the fluid’s ... more

Darcy's law (simplified)

Darcy’s law states that the volume of flow of the pore fluid through a porous medium per unit time is proportional to the rate of change of excess ... more

Area thermal expansion coefficient

Thermal expansion is the tendency of matter to change in length, area or volume in response to a change in temperature, through heat transfer.
The ... more

Heat transfer coefficient

Heat flux or thermal flux is the rate of heat energy transfer through a given surface, per unit surface. The heat transfer coefficient or film coefficient, ... more

Gravitational Potential

In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that is done by the force of ... more

Eb/N0 (the energy per bit to noise power spectral density ratio) is an important parameter in digital communication or data transmission. It is a ... more

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