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Questions and Answers
What type of flow profile is observed in a microchannel with laminar and pressure-driven flow?
What type of flow profile is observed in a microchannel with laminar and pressure-driven flow?
- Parabolic (correct)
- Exponential
- Sine wave
- Linear
In the context of fluid flow, what does the term 'Shear stress' represent?
In the context of fluid flow, what does the term 'Shear stress' represent?
- Flow velocity at the centerline of the microchannel
- Rate of change of pressure with respect to time
- Force per unit area in the direction parallel to flow velocity gradient (correct)
- Pressure at a given point in the fluid
What is the flow profile like in Stokes flow?
What is the flow profile like in Stokes flow?
- Linear (correct)
- Parabolic
- Exponential
- Sine wave
Which type of flow exhibits a velocity profile described by the Poiseuille equation?
Which type of flow exhibits a velocity profile described by the Poiseuille equation?
What is the relationship between shear stress and the rate of change of velocity with respect to distance in a fluid?
What is the relationship between shear stress and the rate of change of velocity with respect to distance in a fluid?
What is the relationship between the decrease of the radius (r0) by a factor of 10 and the increase of fluid resistance (Rfl) in a cylindrical channel, according to the text?
What is the relationship between the decrease of the radius (r0) by a factor of 10 and the increase of fluid resistance (Rfl) in a cylindrical channel, according to the text?
In the context of fluid resistance, if the radius (r0) of a cylindrical channel is quadrupled, how does it affect the fluid resistance (Rfl)?
In the context of fluid resistance, if the radius (r0) of a cylindrical channel is quadrupled, how does it affect the fluid resistance (Rfl)?
How does the Hagen-Poiseuille equation relate to Ohm's Law analogy in the context of fluid dynamics?
How does the Hagen-Poiseuille equation relate to Ohm's Law analogy in the context of fluid dynamics?
What is the specialized term used to describe the resistance to flow in a fluid when it flows through a rectangular channel?
What is the specialized term used to describe the resistance to flow in a fluid when it flows through a rectangular channel?
Which geometry for a channel results in the highest fluid resistance as per the text?
Which geometry for a channel results in the highest fluid resistance as per the text?
In a cylindrical channel, if the length (L) is doubled while keeping other parameters constant, how does it affect the fluid resistance (Rfl)?
In a cylindrical channel, if the length (L) is doubled while keeping other parameters constant, how does it affect the fluid resistance (Rfl)?
In a pressure-driven flow through a microchannel, what is the shape of the velocity profile?
In a pressure-driven flow through a microchannel, what is the shape of the velocity profile?
What is the relationship between shear stress and velocity gradient in a Newtonian fluid?
What is the relationship between shear stress and velocity gradient in a Newtonian fluid?
What is the characteristic length used in the calculation of the Reynolds number for a microchannel flow?
What is the characteristic length used in the calculation of the Reynolds number for a microchannel flow?
In Stokes flow, what is the relationship between the pressure gradient and the velocity profile?
In Stokes flow, what is the relationship between the pressure gradient and the velocity profile?
What is the characteristic feature of Poiseuille flow?
What is the characteristic feature of Poiseuille flow?
In a pressure-driven flow through a microchannel, what is the relationship between the volume flow rate and the pressure difference?
In a pressure-driven flow through a microchannel, what is the relationship between the volume flow rate and the pressure difference?
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Study Notes
Flow Profile of Pressure-Driven Flow in a Microchannel
- Water flow in a microchannel with a diameter of 100 µm, velocity of 0.2 m/s, and Reynolds number of 300 µm has a parabolic flow profile.
- Entrance length (Le) is the distance needed to establish a parabolic flow profile, which is 0.06 times the Reynolds number times the channel diameter.
Hagen-Poiseuille Equation
- The Hagen-Poiseuille equation describes the flow of incompressible fluids in cylindrical tubes and is applicable to laminar flow.
- The equation states that the pressure difference (Δp) is proportional to the volume flow rate (Q), the dynamic viscosity (η), and the length of the tube (L), and inversely proportional to the radius (r0) of the tube.
Flow Characteristics
- In a microchannel, the flow profile for laminar and pressure-driven flow is parabolic.
- Shear stress (τ) is proportional to the derivative of velocity (dv/dy) and is maximum at the channel walls.
- The maximum velocity (vmax) occurs at the center of the channel.
Fluid Resistance
- Fluid resistance (Rfl) is analogous to electrical resistance in Ohm's Law.
- Rfl is proportional to the dynamic viscosity (η), the length of the tube (L), and inversely proportional to the radius (r0) of the tube.
- Decreasing the radius (r0) by a factor of 10 increases Rfl by a factor of 10^4.
Other Channel Types
- For rectangular channels with w ≈ h, the fluid resistance equation is modified to include the width (w) and height (h) of the channel.
- For slit-type channels (w >> h or w << h), the fluid resistance equation is modified accordingly.
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