18 Questions
The Hagen-Poiseuille equation is used to describe the flow profile in microchannels.
True
The Reynolds number is a dimensionless quantity that characterizes the flow regime in microchannels.
True
In microchannels, the entrance length is negligible compared to the channel length for establishing a parabolic flow profile.
False
The characteristic length in microchannels is typically the channel radius.
False
Fully developed flow in microchannels indicates that velocity profiles do not change along the channel length.
True
The inviscid core concept is relevant for describing flows with high viscosity in microchannels.
False
The Hagen-Poiseuille equation is used to calculate the flow rate in a cylindrical channel.
False
According to the Hagen-Poiseuille equation, decreasing the radius of a cylindrical channel by a factor of 10 will result in a decrease of fluid resistance by a factor of 100.
False
The fluid resistance in a cylindrical channel is directly proportional to the length of the channel.
True
The Hagen-Poiseuille equation is analogous to Ohm's Law in electrical circuits.
True
Fully developed flow in microchannels implies that the flow profiles remain constant as the fluid moves along the channel.
True
Inviscid core in fluid mechanics refers to a region within the fluid where viscous effects dominate.
False
In a microchannel, the Stokes equation is simplified for Reynolds number greater than 1.
False
In microfluidics, the Hagen-Poiseuille equation describes the flow profile of pressure-driven flow.
True
The boundary layer thickness increases as the Reynolds number decreases in a microchannel.
False
The inviscid core in a microchannel extends across the entire cross-section of the channel.
False
Fully developed flow in microchannels means that the velocity profile remains constant along the channel length.
True
The pressure gradient in a microchannel with fully developed flow is constant along the channel length.
False
Study Notes
Flow Profile of Pressure-Driven Flow in a Microchannel
- Characteristic length (Le) is a key factor in establishing a parabolic flow profile, where Le = 0.06 × Re × l, and Re is the Reynolds number.
- In a microchannel with a characteristic length of 100 µm, a flow velocity of 0.2 m/s, and water as the fluid, Le ≈ 300 µm.
- The entrance length (Le) is necessary for establishing a parabolic flow profile.
Hagen-Poiseuille Equation
- The Hagen-Poiseuille equation describes laminar flow in a cylindrical channel, where vx(y) = -y × (∆p / (2 × η × L)).
- The equation can be rearranged to solve for ∆p: ∆p = (8 × η × L × Q) / (4 × π × r0^4).
- The Hagen-Poiseuille equation is also applicable to rectangular and slit-type channels with some modifications.
- The fluid resistance (Rfl) is analogous to Ohm's Law, where Rfl = ∆p / Q.
Fluid Resistance
- Fluid resistance (Rfl) in a cylindrical channel is given by: Rfl = (8 × η × L) / (π × r0^4).
- In a rectangular channel, Rfl = (12 × η × L) / (w × h^3) × (1 - Σ((n × π / 2) / h) × tanh(n × π / 2)).
- In a slit-type channel, Rfl is similar to that of a rectangular channel.
Stokes Equation
- The Stokes equation is a simplified version of the Navier-Stokes equation for Re < 1.
- The equation is given by: ∂vx / ∂x = η × ∂^2vx / ∂y^2.
- Solving the equation involves separating variables and applying boundary conditions to find the pressure profile and velocity distribution.
Test your knowledge on the Hagen-Poiseuille equation for flow rate in a cylindrical channel, its rearrangement, and the impact of fabrication tolerances on channel geometries. Explore concepts related to electrical engineering materials and fluid dynamics.
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