Question

# SECTION A: Fluid Mechanics Q1 Figure Q1 shows the arrangement of a sensitive manometer. The reservoirs and tubes between the left-hand side and right-hand side are symmetrical. When PA = PB. the surface of the oil in the two reservoirs are at level of Z above the oil-water interface in the bore tube as shown in Figure Q1(a). When the pressure in reservoir B increases as shown in Figure Q1(b), there will be a respective movement of fluids in the bore tube and reservoirs, denoting the total height differences between the left-hand side and right-hand side in the bore tube as H and the height change in the reservoir as AZ. Oil Water Reservoir A Bore tube Reservoir B Q1(a) PA = PB Z Reservoir A IPA (c) Show that: P-PA (Pw-Po)gH+ Pogh? Ax Bore tube Q1(b) PA < PB Page 4 of 9 Reservoir B N Figure Q1 (a) Based on mass conservation (the volume of fluid displaced in the reservoir must be equal to the volume of fluid displaced in the tube), find the changes in the oil surface Az in reservoir A in relation to H, AT and AR, where AT and AR are the cross-sectional areas of the bore tube and reservoirs, respectively. [2/15 marks] RHS (b) Derive the hydrostatic pressure Plus and PRHS within the fluid in the left and right hand sides of bore tube at the new oil-water interface level of A-A as shown in Figure Q1(b) in relation to PA, PB. g. Pw. Pos Z, H, AT and AR, where g is the gravitational acceleration, Pw is the density of water in the small bore tube, po is the density of oil. [6/15 marks] [7/15 marks]  Fig: 1