pressure difference
Summary
A pressure difference (ΔP) is the pressure at one point minus the pressure at another. It is what drives fluid flow, from higher toward lower pressure. For viscous flow in a tube, flow rate is proportional to ΔP and to r⁴, so small radius changes matter a lot.
Detail
Meaning: Pressure difference, ΔP, is the pressure at one point minus the pressure at another. Fluid is pushed from higher toward lower pressure, because a net pressure force acts on a fluid element only when the pressure on its two sides differs. In a viscous fluid, ΔP along a tube is needed to keep it moving against drag.
Equation: Q = πr⁴ΔP/(8ηL), where Q is volume flow rate (m³/s), r is tube radius (m), ΔP is the pressure difference between the ends (Pa), η is viscosity (Pa·s), and L is tube length (m).
On the MCAT: A passage describes a vessel or pipe that narrows, and you predict the change in flow or in the required ΔP. At fixed ΔP, halving r cuts Q to one sixteenth; at fixed Q, a narrower tube needs a larger ΔP. Hydrostatics uses ΔP = ρgh between two depths, and Bernoulli's equation links a pressure drop to higher speed at a constriction.
Common confusion: Flow depends on the difference, not on the absolute pressure. Equal pressures at the same height give no driving force, however high they are. Also, in a horizontal tube of constant radius with viscous flow, pressure still falls along the tube even though the speed stays constant.
Sources
- Physics (Cutnell and Johnson)
- University Physics (Young and Freedman)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.