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Euler's dimensionless number relates the following
- a)inertial force and gravity
- b)viscous force and inertial force
- c)viscous force and buoyancy force
- d)pressure force and inertial force
Correct answer is option 'D'. Can you explain this answer?
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Euler's dimensionless number relates the followinga)inertial force...
Euler's dimensionless number is a dimensionless parameter used in fluid mechanics to relate pressure force and inertial force. It is denoted by Eu and is defined as the ratio of pressure force to inertial force.
Formula: Eu = (ΔP / ρv²L)
Where,
ΔP = Pressure difference
ρ = Density of fluid
v = Velocity of fluid
L = Characteristic length
Explanation:
In fluid flow, the pressure force and inertial force are the two main forces that play a crucial role in determining the nature of the flow. Euler's dimensionless number relates these two forces and helps in understanding the behavior of the fluid flow.
Inertial force: It is the force that resists the change in motion of the fluid element. It is proportional to the mass of the fluid element and its acceleration. Inertial force is given by the formula F = ma, where F is the force, m is the mass, and a is the acceleration.
Pressure force: It is the force that arises due to the pressure difference between two points in the fluid flow. It is proportional to the pressure difference and the area of the surface on which the force acts. Pressure force is given by the formula F = PA, where F is the force, P is the pressure difference, and A is the area on which the force acts.
Euler's dimensionless number relates these two forces and helps in determining the behavior of the fluid flow. When Eu is less than 1, the pressure force dominates, and the flow is said to be "pressure-driven." When Eu is greater than 1, the inertial force dominates, and the flow is said to be "inertial-driven." When Eu is equal to 1, both forces are equally important, and the flow is said to be "balanced."
Applications:
Euler's dimensionless number is used in various applications in fluid mechanics, such as:
- It is used to determine the nature of the flow, whether it is pressure-driven, inertial-driven, or balanced.
- It is used to analyze the flow of fluids through pipes, channels, and other conduits.
- It is used to design hydraulic systems, such as pumps, turbines, and valves.
- It is used to study the flow of air over aircraft wings, which is essential in aerodynamics.
Formula: Eu = (ΔP / ρv²L)
Where,
ΔP = Pressure difference
ρ = Density of fluid
v = Velocity of fluid
L = Characteristic length
Explanation:
In fluid flow, the pressure force and inertial force are the two main forces that play a crucial role in determining the nature of the flow. Euler's dimensionless number relates these two forces and helps in understanding the behavior of the fluid flow.
Inertial force: It is the force that resists the change in motion of the fluid element. It is proportional to the mass of the fluid element and its acceleration. Inertial force is given by the formula F = ma, where F is the force, m is the mass, and a is the acceleration.
Pressure force: It is the force that arises due to the pressure difference between two points in the fluid flow. It is proportional to the pressure difference and the area of the surface on which the force acts. Pressure force is given by the formula F = PA, where F is the force, P is the pressure difference, and A is the area on which the force acts.
Euler's dimensionless number relates these two forces and helps in determining the behavior of the fluid flow. When Eu is less than 1, the pressure force dominates, and the flow is said to be "pressure-driven." When Eu is greater than 1, the inertial force dominates, and the flow is said to be "inertial-driven." When Eu is equal to 1, both forces are equally important, and the flow is said to be "balanced."
Applications:
Euler's dimensionless number is used in various applications in fluid mechanics, such as:
- It is used to determine the nature of the flow, whether it is pressure-driven, inertial-driven, or balanced.
- It is used to analyze the flow of fluids through pipes, channels, and other conduits.
- It is used to design hydraulic systems, such as pumps, turbines, and valves.
- It is used to study the flow of air over aircraft wings, which is essential in aerodynamics.
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Euler's dimensionless number relates the followinga)inertial force and gravityb)viscous force and inertial forcec)viscous force and buoyancy forced)pressure force and inertial forceCorrect answer is option 'D'. Can you explain this answer?
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