Determine the fluid speed at the origin
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Question
![**Velocity Field in Cartesian Coordinates**
The velocity field of a given flow in Cartesian coordinates can be expressed as:
\[ V = (5z - 3)\hat{i} + (x + 3)\hat{j} + 4y\hat{k} \, \text{ft/s}, \]
where \( x, y, \) and \( z \) are in feet.
**Problem Statement**
Determine the fluid speed at the origin \((0, 0, 0)\) and along the x-axis \((y = z = 0)\).
**Explanation**
- The velocity vector \( V \) consists of three components:
- The \( \hat{i} \) component is \( (5z - 3) \),
- The \( \hat{j} \) component is \( (x + 3) \),
- The \( \hat{k} \) component is \( 4y \).
- To find the speed at a point, compute the magnitude of the velocity vector \( V \).
**Instructions**
1. Substitute the given coordinates into the velocity expression.
2. Calculate the magnitude of the velocity vector accordingly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44dce5c9-bcec-4e4b-a98e-07662a0f3f15%2F677aac8a-912e-4ef4-b5db-0cb4841321da%2F9z1evq7_processed.png&w=3840&q=75)
Transcribed Image Text:**Velocity Field in Cartesian Coordinates**
The velocity field of a given flow in Cartesian coordinates can be expressed as:
\[ V = (5z - 3)\hat{i} + (x + 3)\hat{j} + 4y\hat{k} \, \text{ft/s}, \]
where \( x, y, \) and \( z \) are in feet.
**Problem Statement**
Determine the fluid speed at the origin \((0, 0, 0)\) and along the x-axis \((y = z = 0)\).
**Explanation**
- The velocity vector \( V \) consists of three components:
- The \( \hat{i} \) component is \( (5z - 3) \),
- The \( \hat{j} \) component is \( (x + 3) \),
- The \( \hat{k} \) component is \( 4y \).
- To find the speed at a point, compute the magnitude of the velocity vector \( V \).
**Instructions**
1. Substitute the given coordinates into the velocity expression.
2. Calculate the magnitude of the velocity vector accordingly.
Expert Solution

Given
Velocity Field (V) =
At origin= (0,0,0)
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