Bernoulli’s Equation MCQ Quiz - Objective Question with Answer for Bernoulli’s Equation - Download Free PDF
Latest Bernoulli’s Equation MCQ Objective Questions
Bernoulli’s Equation Question 1:
Given below are two statements :
Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation P1 – P2 = ρg (h2 – h1)
Statement II : In ventury tube shown \(2gh = \nu_1^2 - \nu_2^2\)
In the light of the above statements, choose the most appropriate answer from the options given below.
- Both Statement I and Statement II are correct
- Statement I is incorrect but Statement II is correct
- Both Statement I and Statement II are incorrect
- Statement I is correct but Statement II is incorrect
Answer (Detailed Solution Below)
Option 4 : Statement I is correct but Statement II is incorrect
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Bernoulli’s Equation Question 1 Detailed Solution
Concept:
Bernoulli's equation -
The equation states that the total mechanical energy along a streamline is constant.
\(P_1 + ρ gh_1 + \fracρ v_1^2 = P_2 + ρ gh_2 + \fracρ v_2^2\)
Where, P = The pressure exerted by the fluid at a given point in the flow.
\( \fracρ v^2 \) This represents the kinetic energy per unit volume of the fluid due to its motion.
Calculation:
Applying Bernoulli's equation
\(P_1 + ρ gh_1 + \fracρ v_1^2 = P_2 + ρ gh_2 + \fracρ v_2^2\)
[h1 & h2 are are height of point from any reference level]
Given V1 = V2 = 0 (for statement-1)
\(P_1 + \frac ρ v_1^2 = P_2 + \frac ρ v_2^2\)
\(P_1 - P_2 = \frac\rho v_2^2 - \frac \rho v_1^2\)
\(\rho gh = \frac \rho v_2^2 - \frac\rho v_1^2\)
\(2gh = v_2^2 - v_1^2\)
∴ The correct option is (4)
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Bernoulli’s Equation Question 2:
The expression for Bernoulli’s equation is given by-
- \(P+\fracρ v^2 = constant\)
- \(P+\fracρ v^2 + ρ gh = constant\)
- \(\rho+\fracρ v^2 + ρ gh = constant\)
- \(P+\fracρ v^3 + ρ gh = constant\)
- Not Attempted
Answer (Detailed Solution Below)
Option 2 : \(P+\frac<1>ρ v^2 + ρ gh = constant\)
Bernoulli’s Equation Question 2 Detailed Solution
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
\(P+\fracρ v^2 + ρ gh = constant\)
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
\(P+\fracρ v^2 + ρ gh = constant\)
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.
\(K.E per unit volume = \frac\fracv^2= \fracρ v^2\) 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
