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Test: Hydrostatic Force on Plane Area - Civil Engineering (CE) MCQ


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10 Questions MCQ Test Fluid Mechanics for Civil Engineering - Test: Hydrostatic Force on Plane Area

Test: Hydrostatic Force on Plane Area for Civil Engineering (CE) 2024 is part of Fluid Mechanics for Civil Engineering preparation. The Test: Hydrostatic Force on Plane Area questions and answers have been prepared according to the Civil Engineering (CE) exam syllabus.The Test: Hydrostatic Force on Plane Area MCQs are made for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Hydrostatic Force on Plane Area below.
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Test: Hydrostatic Force on Plane Area - Question 1

A cuboidal beaker is half filled with water. By what percent will the hydrostatic force on one of the vertical sides of the beaker increase if it is completely filled?

Detailed Solution for Test: Hydrostatic Force on Plane Area - Question 1

 Hydrostatic force per unit width on a vertical side of a beaker = 1 ⁄ 2 x  ρgh2,
where ρ = density of the liquid and
h= height of liquid column.
The hydrostatic force when the beaker is completely filled = 1 ⁄ 2 ρg(2h)2 = 2ρgh2.
Thus, percentage increase in hydrostatic force = 
= 300%

Test: Hydrostatic Force on Plane Area - Question 2

Equal volume of two liquids of densities ρ1 and ρ2 are poured into two identical cuboidal beakers. The hydrostatic forces on the respective vertical face of the beakers are F1 and F2 respectively. If ρ1 > ρ2, which one will be the correct relation between F1 and F2?

Detailed Solution for Test: Hydrostatic Force on Plane Area - Question 2

Hydrostatic force per unit width on a vertical side of a beaker = 1 ⁄ 2 x ρgh2,
where ρ = density of the liquid and
h= height of liquid column.
Thus if ρ1 > ρ2, F1 > F2 and F1 ≠ F2, when the h is constant.

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Test: Hydrostatic Force on Plane Area - Question 3

A beaker contains water up to a height of h. What will be the location of the centre of pressure?

Detailed Solution for Test: Hydrostatic Force on Plane Area - Question 3

The depth of the centroid and the centre of pressure yCP are related by:

where I = the moment of inertia and A = area. If = h ⁄ 2; I = bh3/12 ;A = bh, then

Test: Hydrostatic Force on Plane Area - Question 4

A rectangular lamina of width b and depth d is submerged vertically in water, such that the upper edge of the lamina is at a depth h from the free surface. What will be the expression for the depth of the centroid (G)?

Detailed Solution for Test: Hydrostatic Force on Plane Area - Question 4

The centroid of the lamina will be located at it’s centre. ( d ⁄ 2). Thus, the depth of the centre of pressure will be h + d ⁄ 2.

Test: Hydrostatic Force on Plane Area - Question 5

A square lamina (each side equal to 2m) is submerged vertically in water such that the upper edge of the lamina is at a depth of 0.5 m from the free surface. What will be the total water pressure (in kN) on the lamina?
​​​​​​​

Detailed Solution for Test: Hydrostatic Force on Plane Area - Question 5

Total liquid pressure on the lamina = F = ,
where γ = specific weight of the liquid, 
 = depth of centroid of the lamina from the free surface,
A= area of the centroid.
Now, γ = 9:81 x 103 N / m3 
= 0.5 + 1 ⁄ 2  x  2m = 1.5 m,
A = 2 * 2 m2 = 4 m2.
Hence, F = 58.86 kN.

Test: Hydrostatic Force on Plane Area - Question 6

By what factor will the hydrostatic force on one of the vertical sides of a beaker decrease if the height of the liquid column is halved?

Detailed Solution for Test: Hydrostatic Force on Plane Area - Question 6

Hydrostatic force per unit width on a vertical side of a beaker = 1 ⁄ 2  x  ρgh2,
where ρ = density of the liquid and
h= height of liquid column.
Thus, if the liquid column is halved, the hydrostatic force on the vertical face will become one-fourth.

Test: Hydrostatic Force on Plane Area - Question 7

Which of the following is the correct relation between centroid (G) and the centre of pressure (P) of a plane submerged in a liquid?

Detailed Solution for Test: Hydrostatic Force on Plane Area - Question 7

The depth of the centroid and the centre of pressure yCP are related by:

where I = the moment of inertia and A= area. None of the quantities I, A and  can be negative. Thus, YCP > . For horizontal planes, I = 0, hence YCP = 

Test: Hydrostatic Force on Plane Area - Question 8

A cubic tank is completely filled with water. What will be the ratio of the hydrostatic force exerted on the base and on any one of the vertical sides?

Detailed Solution for Test: Hydrostatic Force on Plane Area - Question 8

Hydrostatic force per unit width on a vertical side of a beaker Fv = 1 ⁄ 2  x  ρgh2,
where ρ = density of the liquid and
h= height of the liquid column.
Hydrostatic force per unit width on the base of the beaker = Fb = ρgh  x  h = ρgh2.
Thus, Fb : Fv = 2 : 1.

Test: Hydrostatic Force on Plane Area - Question 9

What is the direction of total liquid pressure on submerged surface?

Detailed Solution for Test: Hydrostatic Force on Plane Area - Question 9

Concept:

  • When a stationary fluid comes in contact with a solid surface either plane or curved, a force is exerted by the fluid on the surface. This force is called total pressure or pressure force or hydrostatic force.
  • Since for a liquid at rest, no tangential force exists, the hydrostatic force acts in the direction normal to the surface.
  • The point of application of total pressure on the surface is called the center of pressure (CP).
  • The direction of total Hydrostatic force (F) on the Horizontal Plane Surface is normal to the surface as it acts in the vertically downward direction. 
Test: Hydrostatic Force on Plane Area - Question 10

In a fluid system, the point of intersection of the line of action of the resultant hydrostatic force and the corresponding surface is known as:

Detailed Solution for Test: Hydrostatic Force on Plane Area - Question 10

Centre of pressure:
The point of intersection of the line of action of the resultant hydrostatic force and the corresponding surface is called the center of pressure. The Centre of pressure is also defined as the point of application of the total pressure on the corresponding surface.

  • According to Pascal’s Law, the pressure or intensity of pressure at a point in a static fluid is equal in all directions.
  • For a plane surface of arbitrary shape immersed in a liquid in such a way that the plane of the surface makes an angle θ with the free surface of the liquid:

A = Total area of an inclined surface, h̅ = Depth of centre of gravity of inclined area from a free surface, h* = Distance of centre of pressure from the free surface of a liquid


For vertical plane surface: θ = 90°

The following facts can be concluded from the above equations:

  • The Center of pressure lies below the centroid because for any plane surface, the factor IG/Ah is always positive
  • The deeper the surface is lowered into the liquid (i.e. greater is the value of h̅), the closer comes the center of pressure to the centroid of the area
  • The depth of the center of pressure is independent of the specific weight of the liquid and is consequently the same for all liquids

Total Pressure:

The total pressure on a surface immersed in a liquid depends on its inclination to the liquid surface.

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