contestada

An 18-meter-tall cylindrical tank with a 4-meter radius holds water and is half full. Find the work (in mega-joules) needed to pump all of the water to the top of the tank. (The mass density of water is 1000 kg/m3. Let g = 9.8 m/s2.

Respuesta :

eve24great2001

Answer:

W = mgh

W = 226290 x 9.8 x 9

W = 19958778Joules

W= 19.958778MegaJoules

Step-by-step explanation:

Work to full the tank is

W = mgh.

m is the mass of the water.

But density = mass/volume, where volume is the volume of the complete the remaining half full of water to fill the cylindrical tank.

mass = density x volume.

Volume of cylinder = πr2h

Volume to fill the cylinder = (πr2h)/2.(half of total volume)

Volume = (22x4x4x9)/(7x2). Height used is 18/2 = 9m

Volume = 226.29m3.

Mass = density x volume= 1000 x 226.29 = 226290kg

Therefore, the work is

W = mgh

W = 226290 x 9.8 x 9

W = 19958778Joule = 19.958778MegaJoules

asuwafohjames

The work needed to pump all of the water to the top of the tank is 39.88 MJ.

What is work?

Work can be defined as the product of force ad distance. The S.I unit of work is Joules (J).

To calculate the work needed to pump the water to the tank, first we need to find the volume of the water in the tank half full.

Formula:

  • V = πr²h/2................ Equation 1

Where:

  • V = Volume of half full water in the tank
  • h = height of the tank
  • r = radius of the base of the tank
  • π = constant called pie

From the question,

Given:

  • r = 4 m
  • h = 18 m
  • π = 3.14

Substitute these values into equation 1

  • V = 3.14(4²)(18)/2
  • V = 452.16 m³.

Finally, to get the work needed to pump all the water to the top of the tank, we use the formula below.

  • W = Vρhg/2................. Equation 2

Where:

  • W = Work needed to pump all the water to the of the tank
  • ρ = Density of the tank
  • h = height of the tank
  • V = Volume of halfull water in the tank
  • g = acceleration due to gravity

From the question.

Given:

  • ρ = 1000 kg/m³
  • h = 18 m
  • g = 9.8 m/s²
  • V = 452.16 m³

Substitute these values into equation 2

  • W = 1000×18×452.16×9.8/2
  • W =  39880512 J
  • W = 39.88 MJ.

Hence, The work needed to pump all of the water to the top of the tank is 39.88 MJ.

Learn more about work here: https://brainly.com/question/8119756

Otras preguntas