流體力學,求流線函數?

2015-12-04 1:00 am
u=1.3+2.8x+t
v=1.5-2.8y
t=0時流線=????
更新1:

有人知道嗎?

回答 (1)

2015-12-05 9:23 pm
u = 1.3 + 2.8x


v = 1.5 - 2.8y


Stream lines: dx/u = dy/v


dx/(1.3 + 2.8x) = dy/(1.5 - 2.8y)


1/2.8* ln(c) = ∫dx/(1.3 + 2.8x) + ∫dy/(-1.5 + 2.8y)


= 1/2.8 * ln(1.3 + 2.8x) + 1/2.8 * ln(-1.5 + 2.8y)



c = (1.3 + 2.8x)(-1.5 + 2.8y)

7.84xy + 2.8(1.3y - 1.5x) - 1.95 - c = 0


Set k = 1.95 + c = Arbitrary constants


Answer: 7.84xy + 2.8*(1.3y - 1.5x) = k


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