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A temperature field T = 5xy^2 is observed in a steady flow with a velocity field V = 2y^2 \hat i...

Question:

A temperature field {eq}T = 5xy^2 {/eq} is observed in a steady flow with a velocity field {eq}V = 2y^2 \hat i + 3x \hat j {/eq}. Calculate the rate of change dT /dt at the point (x, y) = (1,1). All the coordinates are given in meters, temperature in kelvins, and velocities in meters per second.

Rate:

The rate is something that is used to compare one quantity to another quantity. It also determines the change of quantity with respect to another quantity. It will a special type of ratio in which two quantity is present in different units. It is a dimensionless quantity.

Answer and Explanation: 1

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We have given

{eq}T = 5xy^2 {/eq} (Temperature field)

{eq}V = 2y^2 i + 3xj {/eq} (Velocity field)

We know that,

{eq}\dfrac{{dT}}{{dt}} =...

See full answer below.


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How to Find the Unit Rate

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Chapter 50 / Lesson 2
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Unit rates can be helpful for anyone trying to figure out miles per hour, earnings per year, or practically any other amount of one unit it takes for something to happen in other units. In this lesson, take a look at what a unit rate is, why people use unit rates, finding the unit rate, and an example of unit rates.


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