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

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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]