The pressure in a region is given by P(x, y, z) = 1000 + 3x² - 7xy. (i) A wind, flowing from regions of high pressure to low pressure, is evident in the region. The wind direction is parallel/anti-parallel with the pressure gradient. The figure below shows some ar- bitrary contour surfaces of P with vectors indicating the wind direction. Find the wind direction. 2 C 2 -4 2 (ii) A device measuring the directional derivative of the pressure gradient is placed at the position (1, -1, 2) and aligned with the vector m = 2î+5 ĵ−1 ŵ. Find the expected value for the direc- tional derivative. (iii) The pressure can be assumed to be two-dimensional in the plane z = 0. If the measuring device records a directional derivative of -7 at the point (2,1,0) with alignment direction û = u₁₁ + u2ĵ + Ok, find û.
The pressure in a region is given by P(x, y, z) = 1000 + 3x² - 7xy. (i) A wind, flowing from regions of high pressure to low pressure, is evident in the region. The wind direction is parallel/anti-parallel with the pressure gradient. The figure below shows some ar- bitrary contour surfaces of P with vectors indicating the wind direction. Find the wind direction. 2 C 2 -4 2 (ii) A device measuring the directional derivative of the pressure gradient is placed at the position (1, -1, 2) and aligned with the vector m = 2î+5 ĵ−1 ŵ. Find the expected value for the direc- tional derivative. (iii) The pressure can be assumed to be two-dimensional in the plane z = 0. If the measuring device records a directional derivative of -7 at the point (2,1,0) with alignment direction û = u₁₁ + u2ĵ + Ok, find û.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The pressure in a region is given by P(x, y, z) = 1000 + 3x² - 7xy.
(i) A wind, flowing from regions of high pressure to low pressure, is evident in the region. The wind
direction is parallel/anti-parallel with the pressure gradient. The figure below shows some ar-
bitrary contour surfaces of P with vectors indicating the wind direction. Find the wind direction.
2
C
2
-4
2
(ii) A device measuring the directional derivative of the pressure gradient is placed at the position
(1, -1, 2) and aligned with the vector m = 2î+5 ĵ−1 ŵ. Find the expected value for the direc-
tional derivative.
(iii) The pressure can be assumed to be two-dimensional in the plane z = 0. If the measuring device
records a directional derivative of -7 at the point (2,1,0) with alignment direction û = u₁₁ +
u2ĵ + Ok, find û.
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