PRESSURE DEPENDENCE In a fluid of constant density, take two points p, at y1, from the bottom and p2 at y2 from the bottom: dP ρgdy To Generalize: po y2 p = po + ρgh dP ρgdy p y1 p 2 p1 ρg(y2 y1 ) p 2 p1 ρgh p1 p 2 ρgh
Measured from below thesurface; upwardpositive.Measured from thesurface; downwardnegativeMeasured from thesurface; downward positive
The pressure p at a depth h is greater than thepressure po at the same level in the fluid.
• Gauge Pressure – Excess pressure above the atmospheric pressure. p gauge p p atm• Absolute Pressure – Actual Pressure
PASCAL’S PRINCIPLE• “Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. Hydraulic Lift F1 F2 p A2 A2
PRESSURE GAUGESOpen-tube Manometer •The U-shaped tube contains a liquid often water or mercury. •Left end is connected to a container where the pressure will be measured •Right end is open to the atmosphere. p ρgy patm ρgy2 p patm ρg(y2 y1 ) ρgh
PRESSURE GAUGES• Mercury Barometer • Of a long glass tube, closed at one end, that has to filled with mercury and then inverted in a dish of mercury. • Space above the mercury column contains mercury vapor (pressure is very small). • The mercury barometer reads the atmospheric pressure directly from the height of the mercury column