How Does Tube Diameter Affect Reynolds Number in Gravity-Driven Laminar Flow?

In summary, the conversation discusses the relationship between diameter and Reynold's number in fully developed laminar flow of water in a vertical circular tube with atmospheric pressure at the inlet and outlet. The equation D = (32*Re*v2/g)⅓ is derived, where Re is the Reynold's number, v is the velocity of the flow, and g is the gravitational acceleration. In order to use Bernoulli's equation, certain conditions and assumptions must be met, which should be compared to the characteristics of laminar flows and the use of Reynold's number.
  • #1
emac8585
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< Mentor Note -- please remember to use the Homework Help Template when posting schoolwork questions >

Consider the fully developed laminar flow due to gravity of water in a vertical circular tube. Assume atmospheric pressure at inlet and outlet. Show that the relationship between diameter and Reynold's number is

D = (32*Re*v2/g)⅓

I know that Re = ρvD/μ

I was thinking that perhaps I have to use Bernoulli's equation,
v12+P/ρ+gz1 = v22+P/ρ+gz2

But beyond that I'm not sure. Thanks in advance!
 
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  • #2
@emac8585 So what are the things you know about laminar flows and any flow where the Reynolds number makes sense. Then compare that with what you know about Bernoulli's equation and the requirements for its use.
 

Related to How Does Tube Diameter Affect Reynolds Number in Gravity-Driven Laminar Flow?

What is laminar flow due to gravity?

Laminar flow due to gravity is a type of fluid flow where the particles of the fluid move in parallel layers, with little to no mixing or turbulence. This type of flow is caused by the gravitational force acting on the fluid.

How is laminar flow due to gravity different from turbulent flow?

Laminar flow due to gravity is characterized by smooth, orderly movement of fluid particles, while turbulent flow is chaotic and unpredictable. Laminar flow occurs at low velocities and is typically observed in fluids with low viscosity, while turbulent flow occurs at higher velocities and is common in fluids with high viscosity.

What factors affect laminar flow due to gravity?

The viscosity and density of the fluid, as well as the size and shape of the container, can all affect laminar flow due to gravity. Additionally, the velocity and direction of the flow, as well as the presence of any obstacles or barriers, can also impact the flow.

What are some practical applications of laminar flow due to gravity?

Laminar flow due to gravity is commonly used in industries such as chemical and petroleum engineering, where precise and controlled flow of fluids is necessary. It is also utilized in medical procedures, such as intravenous fluid administration and dialysis, and in the design of aircraft and automobiles.

How is laminar flow due to gravity studied and measured?

Scientists and engineers use various techniques to study and measure laminar flow due to gravity, such as using flow visualization methods, mathematical modeling, and physical experiments. Advanced tools like laser Doppler velocimetry and particle image velocimetry can also be used to measure and analyze the flow patterns and characteristics.

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