ALIRAN LAMINER FLUIDA PIPA VERTICAL by Arum Agustiana, Palupi Diah Utami TRKI SV UNDIP

Summary

This video explains the phenomenon of momentum transfer in fluid flow within a vertical pipe. The presenters, Gustina and Palupi, from Industrial Technology, use references from the book *Transport Phenomena* by Bird (Second Edition) to explore fluid dynamics. They discuss fluid behavior in a vertical pipe, focusing on laminar flow, the influence of gravity, pressure differences, and how fluid velocity changes across different layers. The video breaks down complex concepts like momentum balance, shear stress, and differential equations that describe fluid movement. The presentation concludes with a discussion of velocity distribution and average fluid speed.

Takeaways

• 📘 The topic is the phenomenon of momentum transfer in fluid flow through a vertical pipe.
• 👩‍🔬 Presenters are Rumah Gustina from Industrial Engineering and Palupi Dia Utami from Chemical Engineering, both from the 2019 cohort.
• 🔗 The reference for the explanation is Bird's 'Transport Phenomena' (2nd Edition), and a Google Drive link is provided for download.
• 🌊 Fluid flows down a vertical pipe influenced by gravity and pressure difference (pressure at the top is P0, and at the bottom is PL).
• 🧑‍🔬 The fluid flow is laminar, meaning the fluid layers move parallel to each other with the highest velocity in the center of the pipe due to reduced friction.
• 📉 Momentum transfer occurs from the center of the fluid (high velocity) to the outer layers (lower velocity) towards the pipe walls.
• 🔄 A momentum balance is calculated considering forces like gravity and shear stress, leading to a differential equation describing fluid motion.
• 📐 The cylindrical coordinate system is used for solving the problem, with axial (z) and radial (r) directions.
• 🚀 The maximum velocity occurs at the center of the pipe (r=0), and a velocity profile for the fluid is derived from the differential equation.
• ⏳ The average velocity is found to be half of the maximum velocity, and the final velocity distribution equation describes fluid behavior in the vertical pipe.

Q & A

What is the primary focus of the presentation in the script?

The primary focus of the presentation is explaining the phenomenon of momentum transfer in fluid flow through a vertical pipe, particularly under the influence of gravity and pressure differences.

Which reference book is used by the presenters for the explanation?

The presenters refer to the book 'Transport Phenomena' by Bird, Second Edition.

How does gravity influence the fluid flow in the vertical pipe?

Gravity causes the fluid to fall from the top to the bottom of the vertical pipe, impacting the flow by generating a velocity gradient and influencing the momentum transfer from faster-moving layers at the center to slower layers near the pipe walls.

What kind of flow is described in the system, and how is it characterized?

The flow in the system is characterized as laminar, where the fluid layers move parallel to each other with little to no mixing, leading to smooth and steady flow.

Why is the velocity of the fluid highest in the center of the pipe?

The velocity is highest in the center because the fluid near the walls experiences friction, causing resistance and a slower flow. In contrast, the center of the pipe is free from this friction and thus has the highest velocity.

What is the purpose of selecting cylindrical coordinates for the analysis?

Cylindrical coordinates are selected because the pipe is cylindrical in shape. This coordinate system helps in analyzing the velocity and momentum distribution in both the axial (z) and radial (r) directions.

What happens to momentum transfer in the fluid, and how is it explained in the script?

Momentum transfer occurs from regions of high velocity to regions of low velocity, particularly from the center of the pipe towards the pipe walls, as the fluid experiences friction with the pipe surface. This is explained using momentum conservation equations.

What is the relationship between pressure and velocity in the fluid flow described in the script?

As fluid flows down the pipe, there is a pressure difference, with higher pressure at the top (P0) and lower pressure at the bottom (PL). This pressure difference, along with gravity, drives the flow and influences the velocity distribution across the pipe.

What does the script say about the maximum fluid velocity and where it occurs?

The maximum fluid velocity occurs at the center of the pipe (r = 0) due to minimal friction with the pipe walls. The formula for maximum velocity is derived as Vz_max = (P0 - PL) / (4 * μ * L) * R², where R is the pipe radius.

How is the average velocity of the fluid calculated according to the script?

The average velocity is calculated as half of the maximum velocity. The formula for average velocity is Vz_avg = (P0 - PL) / (8 * μ * L) * R², where μ is the fluid's viscosity, and L is the length of the pipe.