belmontes
17.03.2020 •
Engineering
The temperature distribution in a fluid is given by T = 10x + 5y, where x and y are the horizontal and vertical coordinates in meters and T is in degrees centigrade. Determine the time rate of change of temperature of a fluid particle traveling:
(a) horizontally with u = 20 m/s, v = 0.
(b) vertically with u = 0, v = 20 m/s.
(c) diagonally with u = 20 m/s, v = 20 m/s.
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Ответ:
The rates of change of T for each case are the following:
(a) = 200 °C/s
(b) = 100 °C/s
(c) = 300 °C/s
Explanation:
We need to find the rate of change for temperatura of the fluid, which is the derivate of the function as a function of time (t). We know that T is defined as a function of coordinates x and y, but we also know that velocity u is the derivate of x in terms of time (t) of the coordinate x and v is the derivate of y in terms of time (t).
So, to obtain the derivate of T in terms of t, we have:
And, as we said before,
and
Then,
And, as we know the equation that defines T in terms of x and y, we can derivate this function and obtain,
So,
And finally, we replace the value of u and v for each case,
(a) u=20 and v=0
(b) u=0 and v=20
(c) u=20 and v=20
Ответ:
answer:
wth
explanation: