Question

#3 Consider the manometer shown in the figure below, in which a pressure difference PA-PB exists between the two sides of the manometer. Four liquids are in the manometer with densities Pa, PB, pc and pp and the heights of the columns of liquids are shown in the figure. Gravity is pointing downward. PAT B SE What is the pressure at level "1" in terms of the density of the green fluid, PA and ha? What is the pressure at level "la" in terms of PA and the density of the green fluid, PA and ha? What is the pressure at level “2” in terms of Pa and the density of the green and blue fluids and ha and hB? What is the pressure at level 2a in terms of PA and the densities of the green, blue and yellow fluids and ha and he and hc? What is the pressure at level 3 in terms of PA and the densities of the green, blue and yellow fluids and ha and he and hc Find PA-Pg in terms of the heights and densities of all fluids. (iv) (vi) Find FA

Answer 1

pressure p = 8gh X " - 3 P = PAT PAgha 16) -ve] from manometric principle PA + SA gha + Sggn - Sgge = Pia Pia = PatPagha Note: P = Pia PA+ Sa gha + 3892 - Soda - Dog hip = Pv Ü ... Py = PA + Sagha - Sq g h B. siy Pic + Jag ha + fou - $6.97 - Sg Bhg - Seghe = Psa :. Р, • 4 + 0,4, - fsdve -

PA+ Pagha + Pega - Igor & Je gh B - Se ghc - Say +Pegy = Pz - Pg = Pat Pagha + Iz g h B - Seghe (vi) PatsAgha + Sgga - Segla-lg g h B-seghe - Segy 1 tsc gý + f g h - Pg = 0 PA-PB = Sg g h et Seghe - Sagha - Igbo