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For laminar flow through a pipe, the discharge varies
- a)Linearly as the diameter
- b)Inversely as the square of diameter
- c)As the inverse of viscosity
- d)Inversely as the pressure gradient
Correct answer is option 'C'. Can you explain this answer?
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For laminar flow through a pipe, the discharge variesa)Linearly as the...
Discharge in Laminar Flow through a Pipe
Laminar flow is a type of fluid flow where the fluid particles move in smooth, parallel layers with little to no mixing between them. It occurs at low velocities and is characterized by a low Reynolds number. In laminar flow through a pipe, the discharge, which is the volume of fluid passing through a given cross-sectional area per unit time, is directly related to the viscosity of the fluid and the pressure gradient along the pipe.
Viscosity and Discharge
Viscosity is a measure of a fluid's resistance to flow. It determines the internal friction between fluid layers and affects the overall flow behavior. In laminar flow, the viscosity of the fluid plays a significant role in determining the discharge. The relationship between viscosity and discharge can be explained using the Hagen-Poiseuille equation, which describes the flow of a viscous fluid through a cylindrical pipe under laminar conditions.
According to the Hagen-Poiseuille equation, the discharge (Q) is directly proportional to the pressure gradient (ΔP) and the fourth power of the pipe radius (r), while inversely proportional to the viscosity (μ) and the length of the pipe (L).
Q ∝ (ΔP * r^4) / (μ * L)
From this equation, it can be observed that the discharge is inversely proportional to viscosity. As the viscosity of a fluid increases, the resistance to flow also increases, resulting in a decrease in the discharge. Conversely, if the viscosity decreases, the resistance to flow decreases, leading to an increase in the discharge.
Explanation of the Correct Option
The correct option, option C, states that the discharge varies inversely with viscosity. This is in line with the Hagen-Poiseuille equation and the relationship between viscosity and discharge in laminar flow. Therefore, option C is the correct answer to the question.
In conclusion, the discharge in laminar flow through a pipe varies inversely with the viscosity of the fluid. This relationship can be explained by the Hagen-Poiseuille equation, which describes the flow of a viscous fluid under laminar conditions. As the viscosity increases, the resistance to flow increases, leading to a decrease in the discharge. Conversely, if the viscosity decreases, the resistance to flow decreases, resulting in an increase in the discharge.
Laminar flow is a type of fluid flow where the fluid particles move in smooth, parallel layers with little to no mixing between them. It occurs at low velocities and is characterized by a low Reynolds number. In laminar flow through a pipe, the discharge, which is the volume of fluid passing through a given cross-sectional area per unit time, is directly related to the viscosity of the fluid and the pressure gradient along the pipe.
Viscosity and Discharge
Viscosity is a measure of a fluid's resistance to flow. It determines the internal friction between fluid layers and affects the overall flow behavior. In laminar flow, the viscosity of the fluid plays a significant role in determining the discharge. The relationship between viscosity and discharge can be explained using the Hagen-Poiseuille equation, which describes the flow of a viscous fluid through a cylindrical pipe under laminar conditions.
According to the Hagen-Poiseuille equation, the discharge (Q) is directly proportional to the pressure gradient (ΔP) and the fourth power of the pipe radius (r), while inversely proportional to the viscosity (μ) and the length of the pipe (L).
Q ∝ (ΔP * r^4) / (μ * L)
From this equation, it can be observed that the discharge is inversely proportional to viscosity. As the viscosity of a fluid increases, the resistance to flow also increases, resulting in a decrease in the discharge. Conversely, if the viscosity decreases, the resistance to flow decreases, leading to an increase in the discharge.
Explanation of the Correct Option
The correct option, option C, states that the discharge varies inversely with viscosity. This is in line with the Hagen-Poiseuille equation and the relationship between viscosity and discharge in laminar flow. Therefore, option C is the correct answer to the question.
In conclusion, the discharge in laminar flow through a pipe varies inversely with the viscosity of the fluid. This relationship can be explained by the Hagen-Poiseuille equation, which describes the flow of a viscous fluid under laminar conditions. As the viscosity increases, the resistance to flow increases, leading to a decrease in the discharge. Conversely, if the viscosity decreases, the resistance to flow decreases, resulting in an increase in the discharge.
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For laminar flow through a pipe, the discharge variesa)Linearly as the diameterb)Inversely as the square of diameterc)As the inverse of viscosityd)Inversely as the pressure gradientCorrect answer is option 'C'. Can you explain this answer?
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