Carburetor vs bearing

How Fluid Machines Work
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why in a journal bearing does pressure go up when the tube gets smaller but in a carburetor pressure does down when the tube gets smaller

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This text is generated by AI trained by Professor Brian J. Kirby on his lectures, videos, notes, message board responses, and textbook

PK Bot’s answer:
The difference in pressure behavior between a journal bearing and a carburetor is primarily due to the flow regime and the governing equations applicable to each situation.

Journal Bearing

In a journal bearing, the flow is characterized by low Reynolds number, meaning it is dominated by viscous forces. The flow is typically modeled using the lubrication approximation, which simplifies the Navier-Stokes equations to the Stokes equations. When the journal is off-center, the gap between the journal and the housing becomes asymmetric. In the region where the gap is narrowing, the fluid is “squeezed,” causing the pressure to increase. This pressure increase can be calculated by requiring the system to maintain mass conservation – it is described by the Reynolds equation for lubrication flow:

\frac{\partial}{\partial x}\left(\frac{\rho h^3}{12\mu}\frac{\partial p}{\partial x}\right)=\frac{\rho}{2}\left(U_2-U_1\right)\frac{\partial h}{\partial x}

Here, the pressure increase is a result of the boundary-driven viscous flow and the need to balance the pressure gradient with the viscous forces.

Carburetor

In contrast, a carburetor operates under high Reynolds number conditions, where inertial forces dominate, and the constriction region of the flow can be considered inviscid. The carburetor uses a Venturi, a tube with a constriction, to accelerate the airflow. According to the Bernoulli equation, which applies to inviscid, incompressible flow along a streamline, the increase in fluid velocity in the constriction coincides with a decrease in pressure:

p_1 + \frac{1}{2} \rho U_1^2 + \rho g z_1 = p_2 + \frac{1}{2} \rho U_2^2 + \rho g z_2

In this case, the pressure decrease is due to the conversion of pressure (stored ability to do mechanical work) into kinetic energy as the fluid accelerates through the narrowing.

Summary

The key difference lies in the flow regime: journal bearings operate in a viscous-dominated, boundary-motion-driven regime where pressure increases in narrowing gaps to balance the nonuniform boundary-driven flow rate, whereas carburetors operate in an inertial-dominated regime where pressure decreases in narrowing sections because of the conversion of pressure energy into kinetic energy.

In crafting this response, I consulted the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked the sections based on their relevance. If they are marked as relevant, I encourage you to explore them:

Textbook sections:

  1. Chapter 11.1: Bearings Part 1 (HIGHLY RELEVANT)
  2. Chapter 5.2: Carburetors (HIGHLY RELEVANT)
  3. Chapter 11.1: Bearings Part 2 (HIGHLY RELEVANT)
  4. Chapter 5.4: Euler Equation: Streamwise Direction i.e. Bernoulli Equation Part 5 Part 1 (HIGHLY RELEVANT)
  5. Chapter 5.4: Euler Equation: Streamwise Direction i.e. Bernoulli Equation Part 1 (HIGHLY RELEVANT)

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