What is the resultant force exerted by the sides of the glass on the water?

In summary, the water in a glass has a bottom of area 20 cm 2 , top of area 20 cm 2 , height 20 cm and volume half a litre. The pressure at the bottom is 204 N and the weight of the water is 5 N. The side walls of the glass exert a force of 1 N to keep the water in equilibrium.
  • #1
lavankohsa
32
0

Homework Statement


A glass full of water has a bottom of area 20 cm 2 , top of area 20 cm 2 , height 20 cm and volume half a litre.
(a) Find the force exerted by the water on the bottom. (b) Considering the equilibrium of the water, find the
resultant force exerted by the sides of the glass on the water. Atmospheric pressure = 1'0 x 10 N/m 2 . Density
of water = 1000 kg/m 3 and g = 10 m/s 2 . Take all numbers to be exact

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Homework Equations

The Attempt at a Solution


I calculated the first part by pressure at bottom*area of bottom. But i am not able to solve the 2nd part. Please help.
 
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  • #2
It looks like you did the first part correctly. Now, to do the second part, start by drawing a free body diagram on the water in the container (which is in equilibrium). What are the forces acting on the water?

Chet
 
  • #3
For first part i found out the pressure at the bottom which is Patm+density*g*h and multiply it by base area. The answer i got 204 N.
Now for 2nd part i calculated the weight of water (vol*density) which is 5N. I drew below diagram,

6em7tu.jpg
 
  • #4
You are very close to having the answer. What is the downward force exerted by the air on the top of the water? What is the upward force exerted by the bottom of the vessel on the water? You already got 5 N for the weight of the water (the downward force of gravity on the water). What force does the side walls of the vessel have to exert on the water (and in what direction) to keep the water in equilibrium? This is determined by your overall force balance in the vertical direction.

As an aside, your diagram looks very nice (especially the directions of the arrows), but the lengths of the arrows should be getting longer as you go from the top of the vessel to the bottom of the vessel. Do you know why?

Chet
 
  • #5
Will the normal force of base will be 204 N or weight of water which is 5 N ?? I know the arrow should be longer as we move down because pressure increases as we go down.
 
  • #6
Ok i solved it i guess. The normal force will be 204 N. Suppose the force by the side wall is F(upward). So for equilibirium,

Patm*A+weight of water=N+F.

1*105*20*10-4+5=204+F

205=204+F

so F=1N
 
  • #7
lavankohsa said:
Ok i solved it i guess. The normal force will be 204 N. Suppose the force by the side wall is F(upward). So for equilibirium,

Patm*A+weight of water=N+F.

1*105*20*10-4+5=204+F

205=204+F

so F=1N
Why do you say "I guess." Do you not feel like you understand it to the extent that you would like, or do you feel that I helped too much?

Chet
 
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Likes lavankohsa

1. What is fluid mechanics?

Fluid mechanics is the branch of physics that studies how fluids (liquids and gases) behave and interact with their surroundings. It involves studying the forces and pressures acting on fluids and how they move and flow in different situations.

2. How is pressure defined in fluid mechanics?

Pressure is defined as the force per unit area acting on a surface. In fluid mechanics, pressure is the force exerted by a fluid on the walls of its container or on any object placed within the fluid. It is typically measured in units of Pascals (Pa) or Newtons per square meter (N/m²).

3. What factors affect fluid pressure?

The three main factors that affect fluid pressure are the density of the fluid, the acceleration due to gravity, and the depth at which the fluid is located. As the density or depth increases, the pressure also increases. The effect of gravity on pressure is more complex and depends on the direction and speed of fluid flow.

4. How is fluid pressure related to fluid motion?

In fluid mechanics, there is a direct relationship between pressure and fluid motion. When a fluid is in motion, it experiences different pressures at different points due to the forces acting on it. This pressure difference causes the fluid to move from areas of high pressure to areas of low pressure, resulting in fluid flow.

5. What are some practical applications of fluid mechanics?

Fluid mechanics has many practical applications in our daily lives, such as in the design of pumps, turbines, and engines. It is also used in the fields of aerodynamics and hydrodynamics to study the movement of air and water, which is important in the design of airplanes, ships, and cars. Additionally, fluid mechanics is crucial in understanding weather patterns and predicting natural disasters like hurricanes and tsunamis.

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