Bernoulli’s Equation MCQ Quiz in मल्याळम - Objective Question with Answer for Bernoulli’s Equation - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

CONCEPT:

Bernoulli's principle:

• The total mechanical energy of the moving fluid comprising the gravitational potential energy of elevation, the energy associated with the fluid pressure, and the kinetic energy of the fluid motion, remains constant.
• According to Bernoulli's principle,

​\(\Rightarrow P_1+\frac{1}{2}ρ v_1^2+ρ gh_1=P_2+\frac{1}{2}ρ v_2^2+ρ gh_2\)

Where P1, v1, and h1 = pressure, velocity, and elevation of point 1 respectively, P2, v2, and h2 = pressure, velocity, and elevation of point 2 respectively, ρ = density of flowing fluid, and g = gravitational acceleration

Blood flow and heart attack:

• Bernoulli’s principle helps in explaining blood flow in arteries.
• The artery may get constricted due to the accumulation of plaque on its inner walls. In order to drive the blood through this constriction, a greater demand is placed on the activity of the heart.
• The speed of the flow of the blood in this region is raised which lowers the pressure inside and the artery may collapse due to the external pressure.
• The heart exerts further pressure to open this artery and forces the blood through.
• As the blood rushes through the opening, the internal pressure once again drops due to the same reasons leading to a repeat collapse. This may result in a heart attack.

EXPLANATION:

• We know that Bernoulli’s principle helps in explaining blood flow in arteries. Hence, option 2 is correct.

CONCEPT:​

Magnus effect:

• The force exerted on a rapidly spinning cylinder or sphere moving through air or another fluid in a direction at an angle to the axis of spin is called the Magnus effect.
• This force is responsible for the swerving of balls when hit or thrown with spin.

Strokes law:

• When a body falls through a fluid it drags the layer of the fluid in contact with it.
  • A relative motion between the different layers of the fluid is set and, as a result, the body experiences a retarding force. 
  • It is seen that the viscous force is proportional to the velocity of the object and is opposite to the direction of motion.
  • The other quantities on which the force F depends are viscosity η of the fluid and radius (a) of the sphere, the viscous drag force F:

⇒ F = 6 π η a v

• Viscosity: Viscosity is the resistance offered by a fluid to its motion

EXPLANATION: 

• Dynamic lift is the force that acts on a body, such as an airplane wing, a hydrofoil, or a spinning ball, by virtue of its motion through a fluid. 
• The dynamic lift due to spinning is called the Magnus effect.  Hence option 3 is correct.

CONCEPT :

• Bernoulli's principle states that the sum of pressure energy, kinetic energy, and potential energy per unit volume of an incompressible, non- viscous fluid in a streamlined irrotational flow remains constant along a streamline.
• This means that in steady flow the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline.

\(P+\frac{1}{2}ρ V^{2}+ ρ gh = \ A \ constant\)

EXPLANATION:

• During certain wind storm or cyclone, the roofs of some houses are blown off without damaging the other parts of the house.
• The high wind blowing over the roof creates a low-pressure P₂, in accordance with Bernoulli's principle. 
• The pressure P₁ below the roof is equal to the atmospheric pressure which is larger than P₂.
• The difference of pressure (P₁ - P₂) causes an upward thrust and the roof is lilted up.
• Once the roof is lifted up, it is blown off with the wind.

CONCEPT:

Bernoulli's principle: For a streamlined flow of an ideal liquid in a varying cross-section tube the total energy per unit volume remains constant throughout the fluid.

• This means that in steady flow the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline.

From Bernoulli's principle

\({{\rm{P}}_1} + {\rm{\rho \;g\;}}{{\rm{h}}_1} + \frac{1}{{2{\rm{\;}}}}\rho \;{\rm{v}}_1^2 = {{\rm{P}}_2} + {\rm{\rho \;g\;}}{{\rm{h}}_2} + \frac{1}{2}{\rm{\rho \;v}}_2^2\)

option(2)

CONCEPT:

• Bernoulli's Principle is given by Swiss physicist Daniel Bernoulli derived an expression relating the pressure to fluid speed and height in 1738.

• It states that the sum of the pressure energy, kinetic energy, and potential energy per unit volume of an incompressible, non-viscous fluid in a streamlined flow remains constant.

It can be expressed as Mathematically:

\(P+\frac{1}{2}ρ v^2 + ρ gh = constant\)

Where P is pressure in the fluid, ρ is the density of the fluid, h is the mean height, g is the acceleration due to gravity.

• Bernoulli's Principle is based on the Law of conservation of Energy.

EXPLANATION:​

• Bernoulli's principle is based on the law of Conservation of Energy.
• Hence option 2 is correct.

Additional Information

• Conservation Of Energy states that energy neither be created nor be destroyed it can only be transferred from one body to another body.
• Pressure Energy: pressure energy is the energy of a fluid due to the applied pressure
• Kinetic Energy per unit volume is the type of energy that is responsible to make the particle of the fluid movement.

\(K.E per unit volume = \frac{1}{2}\frac{M}{V}v^2= \frac{1}{2}ρ v^2\) 

Where M/V is density, v is the velocity of the fluid, ρ is the density of the fluid.

• Potential Energy is the type of energy that is stored in an object due to its position relative to some zero position.

CONCEPT:

• Bernoulli's Principle: It states the total mechanical energy of the moving fluid comprising the energy associated with the fluid pressure (P), the gravitational potential energy of elevation ρgh, and the kinetic energy of the fluid motion \({1\over 2}ρ v^2 \), remains constant. i.e. 

\(P+ {1\over 2}ρ v^2 +ρ g h= const.\)

Where p is the pressure exerted by the fluid, v is the velocity of the fluid, ρ is the density of the fluid, h is the height of the container.​

• Dimensional formula: It is a compound expression that shows which of the fundamental quantities and how are they involved in making of a physical quantity.
• The dimension's principle of homogeneity says that an equation is dimensionally correct only if each term has the same dimension on both sides of the equation.

EXPLANATION:

Given equation is \(P+ {1\over 2}ρ v^2 +ρ g h= K (const.)\)

So, the dimension of [P] will be equal to the dimension of [\( {1\over 2}ρ v^2 \)] and [\(ρ g h\)] and \( K (const.)\)

\([P]= [{1\over 2}ρ v^2] =[ρ g h]= [K]\)

The dimension of [P]  = The dimension of [K]

So the dimension of \([{P\over K}]\) = dimensional less or no dimension.

• There the quantity \({P\over K}\) is a dimensionless quantity.
• Hence the correct answer is option 4.

CONCEPT:

• Bernoulli's Principle: It states the total mechanical energy of the moving fluid comprising the energy associated with the fluid pressure (P), the gravitational potential energy of elevation ρgh, and the kinetic energy of the fluid motion \({1\over 2}ρ v^2 \), always remains constant. i.e. 

\(P+ {1\over 2}ρ v^2 +ρ g h= const.\)

Where p and v are the pressure exerted by the fluid and the velocity of the fluid respectively, ρ is the density of the fluid, h is the height of the container.

• Bernoulli's Principle basically states energy conservation for fluids.

EXPLANATION:

• Bernoulli's Principle basically states energy conservation for fluids.

\(P+ {1\over 2}ρ v^2 +ρ g h= const.\)

Using Bernoulli's Principle at Points A and B.

\(P_A+ {1\over 2}ρ v_A^2 +ρ g h_A= P_B+ {1\over 2}ρ v_B^2 +ρ g h_B\)

P_A = P_B (Since both are at the atmospheric level)

\( {1\over 2}ρ v_A^2 +ρ g h_A= {1\over 2}ρ v_B^2 +ρ g h_B\)

\( {1\over 2} v_A^2 + g h_A= {1\over 2} v_B^2 +g h_B\)

At point B there will be no velocity. So v_B = 0

At point A taking ground position, so h_A = 0; h_B = H

\( {1\over 2} v_A^2 + g\times 0= {1\over 2} 0^2 +g h_B\)

\( {1\over 2} v_A^2 =g h_B\)

\( {1\over 2} 4^2 =10\times H\)

H = 0.8 m

• So water will rise up to 0.8 m.
• Hence the correct answer is option 3.

CONCEPT:

• Bernoulli’s theorem is proved by making some assumptions.

These assumptions are:

• Liquid is incompressible
• Liquid is non-viscous
• The velocity of a particle is uniform
• Steady flow

The CGS unit of viscosity is poise

1 poise = 0.1 Pa s

The equation of continuity is A₁V₁ρ₁ = A₂V₂ρ₂  

EXPLANATION:

• Option 1 is correct as we know the limitation of Bernoulli's theorem is- it is valid for a particle having a uniform velocity.
• Option 2 is correct CGS unit of viscosity is poise

Option 3 is correct Equation of continuity is - A1V1ρ1 = A2V2ρ2 . 

Here ρ₁ = ρ₂  So, we can say that A1V1 = A2V2

So, all three options are correct that’s why Option 4 is followed.

Additional Information

Bernoulli's equation: It states that the total energy of the incompressible and non-viscous fluid in steady flow through a pipe remains constant.

\(\frac{P}{ρ}+gh+\frac{1}{2}v^{2} = Constant\) 

Where, P = Pressure of liquid, ρ = Density of liquid

CONCEPT:

• Bernoulli’s principle states that: The increase in the speed of a fluid flowing leads to the decrease in static pressure of the fluid.
• The total mechanical energy of a flowing fluid having gravitational potential energy, the energy associated with the fluid pressure and the kinetic energy of the fluid movement, remains constant.

\(P+\rho ~g~h+~\frac{1}{2}\rho ~{{V}^{2}}=constant\)

Where P is pressure, V is the velocity of flow of fluid, h is height, g is the acceleration due to gravity and ρ is the density of the fluid

EXPLANATION:

• According to the definition of Bernoulli’s principle, the total mechanical energy remains constant which is basically the conservation of energy. Hence option 4 is correct.

CONCEPT:

• Bernoulli's Principle is given by Swiss physicist Daniel Bernoulli derived an expression relating the pressure to fluid speed and height in 1738.
• Bernoulli's Principle is based on the Law of conservation of energy, which can be expressed as

​
\(P+\frac{1}{2}ρ v^2 + ρ gh = constant\)

EXPLANATION:

• Bernoulli's Principle states that the sum of the pressure energy, kinetic energy, and potential energy per unit volume of an incompressible, non-viscous fluid in a streamlined flow remains constant.

It can be expressed as Mathematically

\(P+\frac{1}{2}ρ v^2 + ρ gh = constant\)

Where P is pressure in the fluid, ρ is the density of the fluid, h is the mean height, g is the acceleration due to gravity.

• The above formula is based on the law of Conservation of Energy.

Additional Information

• Law of Conservation of energy states that energy can neither be created nor destroyed it can only be transferred from one form of energy to another.
• Pressure Energy  pressure energy is the energy of a fluid due to the applied pressure
• Kinetic Energy per unit volume is the type of energy that is responsible to make the particle of the fluid movement.

\(K.E per unit volume = \frac{1}{2}\frac{M}{V}v^2= \frac{1}{2}ρ v^2\) where M/V is density, v is the velocity of the fluid, ρ is the density of the fluid.

• Potential Energy is the type of energy possessed by a liquid by virtue of its position above the earth's surface.

​P.E per unit volume = mgh/V = ρgh