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Chapter 14: Q4Q (page 405)

Figure 14-22 shows a tank filled with water. Five horizontal floors and ceilings are indicated; all have the same area and are located at distances L, 2L, 3Lorbelow the top of the tank. Rank them according to the force on them due to the water, greatest first.

Short Answer

Expert verified

The rank of floors according to the force on them due to the water, greatest first is

Fe>Fb=Fd>Fa=Fc.

Step by step solution

01

The given data 

  1. Heights of floors from top of tank: he>hb=hd>ha=hc
  2. All floors have same area and are at distances, L ,2L or 3L below the top of the tank.
02

Understanding the concept of force and pressure

Pressure due to fluid is directly proportional to the depth from the surface of the water. Now, using this relation value of pressure and depth, we can get the behavior of the force on the body that is related to pressure.

Formula:

The gauge pressure on the body, p=蚁gh (i)

The force applied on a body due to the pressure,F=pA (ii)

03

Calculation of the rank of the floors according to their force

Substituting the value of gauge pressure on a body of equation (i) in equation (ii), we can get the value of the force

F=蚁ghA

Since area is thesame for all the surfaces, force is directly proportional to the height from the top of thetank.

Therefore, the rank according to the force on floors due to water isFe>Fb=Fd>Fa=Fc.

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