Q 11. If the velocity of a flow of a g... [FREE SOLUTION]

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Chapter 14: Q 11. (page 1131)

If the velocity of a flow of a gas at a point (x, y, z) is represented by F and the gas is expanding at that point, what does this imply about the divergence of F at the point?

Short Answer

Expert verified

$The gas is expanding at that point, so the divergence of F at that point (x, y, z) will be positive .$

Step by step solution

Step 1. Given information is

Velocity of a flow of a gas at a point (x, y, z) is F and the gas is expanding at that point

Step 2. Divergence of F

$If F (x, y, z) = F_{1} (x, y, z) i + F_{2} (x, y, z) j + F_{3} (x, y, z) k is a vector field, then the divergence of the vector field is defined as follows : 鈭� . F = \frac{鈭� F_{1}}{鈭� x} + \frac{鈭� F_{2}}{鈭� y} + \frac{鈭� F_{3}}{鈭� z} Note that value of 鈭� . F is scalar . Here, the divergence of F, that is, 鈭� . F at a point of F measures the magnitude of the rate of change of the vector field away from a source or towards a sink . If F represents the flow of a gas, then the sign of this scalar 鈭� . F corresponds to whether the gas is compressing (鈭� . F is negative) or expanding (鈭� . F is positive) . In this case, the gas is expanding at that point, so the divergence of F at that point (x, y, z) will be positive .$

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91影视

If the velocity of a flow of a gas at a point (x, y, z) is represented by F and the gas is expanding at that point, what does this imply about the divergence of F at the point?

Short Answer

Step by step solution

Step 1. Given information is

Step 2. Divergence of F

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