Pressure gradient, abbreviated as \(\nabla p\), is the rate of change of pressure with respect to distance. It is typically used to describe pressure variations within a fluid that is not in hydrostatic equilibrium. The pressure gradient vector points in the direction where the pressure increases most rapidly. However, in many fluid dynamics contexts, we're interested in the direction of decreasing pressure because fluids flow from high pressure to low pressure.
Key Points about Pressure Gradient
High Pressure Gradient - Indicates a rapid change in pressure over a short distance, which can lead to high velocities in fluid flow or strong winds in atmospheric contexts.
Low Pressure Gradient - A more gradual change in pressure, leading to slower flow rates or milder weather conditions in meteorology.
Low Pressure Gradient - A more gradual change in pressure, leading to slower flow rates or milder weather conditions in meteorology.
Pressure Gradient Applications
Meteorology - In weather systems, the pressure gradient force drives wind from areas of high pressure to areas of low pressure.
Fluid Mechanics - In pipes or channels, the pressure gradient along the flow direction is a primary driver of fluid movement.
Hydrology - It influences groundwater flow, where water moves from regions of higher hydraulic head (pressure) to lower.
Medicine - In blood flow, the pressure gradient across vessels like arteries or veins helps in understanding circulation.
Pressure Gradient Formula |
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\( \nabla p \;=\; \dfrac{ \Delta p }{ \Delta l } \) (Pressure Gradient) \( \Delta p \;=\; \nabla p \cdot \Delta l \) \( \Delta l \;=\; \dfrac{ \Delta p }{ \nabla p } \) |
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| Symbol | English | Metric |
| \( \nabla p \) = Pressure Gradient | \(psi\;/\;ft\) | \(Pa\;/\;m\) |
| \( \Delta p \) = Pressure Change | \(lbf\;/\;in^2\) | \(Pa\) |
| \( \Delta l \) = Distance Over which the Change Occurs | \(ft\) | \(m\) |
