Question

PIUVICU JEU 12, DUC 24 JCPECHuel 201 1. Given a temperature field defined the function T = 280.0 +0.002x +0.004y2 +0.00982, compute the change in temperature for a displacement of 100m in the northwesterly direction and 50m in the vertical direction 2. If VT is the gradient of temperature, show that the maximum variation of T associated with displacement dS occurs when the displacement vector is in the same direction as the gradient. 3. Chart the vector fields defined by the following functions: (a) U = ix+jy: (b) Ü = -ix - jy and (c) Ū = ix + jy + kz. Discuss the spatial variability of these vector fields utilizing appropriate vector operators 4. Consider the following funtion for three dimensional velocity field U = 16(xy + y) + j(x - y) + ko. Is this flow field divergent or rotational?

Answer 1

T= 280+ 0.0020² +0.004 g + o. 0092, 100 Te at T (100, 100, 50) I, at T (0, 0, 0) 160,000 & Ti = 280 T2= 280+ 20 + 40 +0,49 z = 310,49 AT-T2-T1 = 310.49- 280 = 30.49 2) дх let a small displacement vector be ds = dc ? + dy h + dzk Ita + FIA Vì s = PT A C = 4T so dT is maximum when los o=1 or no = ds is along dish of IT.

3) а) = (х + ) у D) 1 - 0 - 25 с) - zf + ул. за

y = 6lxgry? ) ( + (x²y3) g T. U = dui + 2 Uj by +(-2y) = My Ja dy i. J.5 = 4y . How is divergent JXU = | 7 =(0)-910) +R(2x - 6x= 123 1 blngrge x = y ² o x3 = 124-4 this rotational too