Manometers Open Devices for pressure measurement Piezometer tube(stand pipe Simple u-tube Differential u-tube manometer Inclined tube manometer Other types Micro-manometer Barometer
Manometers Devices for pressure measurement : • Piezometer tube (stand pipe) • Simple U-tube • Differential U-tube manometer • Inclined tube manometer Other types : • Micro-manometer • Barometer
Manometer calculation Within a continuous fluid of constant p 1"pg Ah 1y4h, P4=P1+pg^h2=P1+y△h Start computation at one end, and compute pressure from meniscus to meniscus till the other end Alternatively, select two points along same liquid column at same level, equate the pressures at the two points
Manometer Calculation Within a continuous fluid of constant P1 = P3 P2 = P1 - g h1 = P1 - h1 P4 = P1 + g h2 = P1 + h2 • Start computation at one end, and compute pressure from meniscus to meniscus till the other end • Alternatively, select two points along same liquid column at same level, equate the pressures at the two points h1 h2 P1 P2 P3 P4
Piezometer tube Open A gauge g hy (1) Simple u-manometer Open A+ pigh =pgh A gauge-p2g h2-P1gh1 x(1) h2 (2) (3)
Piezometer Tube PA.gauge = g h1 Simple U-Manometer P2 = P3 PA + 1gh1 = 2 g h2 PA,gauge = 2 g h2 - 1gh1
Differential u-tube PA+ pigh1-p2gh2-P3gh3 h2 aPb= P2gh2 t p3gh3-pghI (1) Inclined manometer Pipes a b contain gas PA-P2gl2 sin 0=pb PA-Pb= l sin e
Differential U-tube PA + 1 g h1 - 2gh2 - 3gh3 = PB PA – PB = 2gh2 + 3gh3 - g h1 Inclined Manometer Pipes A & B contain gas PA - 2 g l2 Sin = PB PA – PB = 2 g l2 Sin
Pressure and force on a small plane area Pressure on plane P mall plane area da Pressure at small plane P=pg h Force on small plane dF=px da=pghda Depends on vertical depth h below surface Force dF= px plane area P and df perpendicular to plane
Pressure and force on a small plane area Pressure at small plane : P = g h Force on small plane dF = P x dA = g h dA P depends on vertical depth h below surface Force dF = P x plane area P and dF perpendicular to plane Pressure on plane P h Small plane area dA