In a static (stationary) fluid, the z-axis points vertically upward and the x-axis is horizontal. If d denotes the density of the fluid, which of the following correctly describes the pressure gradient?

dp/dz = -dg
dp/dx = dg
dp/dx = 0
dp/dz = 0

Correct answer: dp/dz = -dg

Solution

In a static fluid the pressure gradient along the vertical direction satisfies dP/dz = -rho*g (pressure decreases upward), while there is no pressure variation in the horizontal direction (dP/dx = 0). Option A states the correct vertical relation; note that option C is also true, but A directly gives the defining hydrostatic equation.

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