Show that when laminar flow occurs with mean velocity um between extensive stationary flat plates the mean kinetic energy divided by mass of the fluid is 1.543 um/2.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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**Title: Understanding Kinetic Energy in Laminar Flow Between Stationary Plates**

**Text:**
Show that when laminar flow occurs with mean velocity \( u_m \) between extensive stationary flat plates, the mean kinetic energy divided by the mass of the fluid is \( 1.543 \, \frac{u_m^2}{2} \).

**Explanation:**
This statement addresses the dynamics of laminar flow, specifically the relationship between velocity and kinetic energy. When fluid moves in a laminar pattern between two flat surfaces, each layer of fluid flows smoothly in parallel without turbulence. Here, the mean kinetic energy per unit mass of this flowing fluid is calculated to be slightly higher than half the square of the mean velocity, scaled by a factor of 1.543, indicating a specific energy distribution profile for such flow conditions.
Transcribed Image Text:**Title: Understanding Kinetic Energy in Laminar Flow Between Stationary Plates** **Text:** Show that when laminar flow occurs with mean velocity \( u_m \) between extensive stationary flat plates, the mean kinetic energy divided by the mass of the fluid is \( 1.543 \, \frac{u_m^2}{2} \). **Explanation:** This statement addresses the dynamics of laminar flow, specifically the relationship between velocity and kinetic energy. When fluid moves in a laminar pattern between two flat surfaces, each layer of fluid flows smoothly in parallel without turbulence. Here, the mean kinetic energy per unit mass of this flowing fluid is calculated to be slightly higher than half the square of the mean velocity, scaled by a factor of 1.543, indicating a specific energy distribution profile for such flow conditions.
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