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Foundations of Fluid Mechanics Tutorial 2 - on Fluid Statics

Q (1*) Determine p between points A and B as shown in FIG 1. Take all fluids to be at 20C. Specific

weights for Benzene: 8640 N/m3 Mercury: 133100 N/m3 Kerosene: 7885 N/m3 Water: 9790 N/m3

and for air :12 N/m3.

FIG 1 FIG 2 FIG 3

Q (2) A bottle of liquid (SG = 0.96) is under pressure as shown in FIG 2. This is connected to a

mercury manometer for reading. Compute the net force on the 2-in-radius hemispherical end cap at

the bottom of the bottle Water Sp. Wt. = 62.4 lbf/ ft3

Q (3*) A capped oil well drilled to a depth of h = 4,000 m terminates in a pool of oil that has filled the

well completely to the surface, where the well head gage pressure of oil is measured to be 3x106 Pa.

(a) If the oil has a density of 950 kg/m3, what is the oil gage pressure p2 at the bottom of the well ?

(b) Drilling mud is a fluid with a density, that can be adjusted to any value greater than that of water.

In order to continue drilling below 4000 m, the drilling crew will pump drilling mud into the well to

displace the oil. Calculate the density of the mud needed if the well head gage pressure is to be

reduced to zero when the well is completely filled with mud.

Q (4) Determine the change in hydrostatic pressure in a Giraffes head as it lowers its head from

eating leaves 6 m above the ground to getting a drink of water at ground level. Assume SG of blood =

1.0. Compare this value of pressure change against the normal 120 mm of Hg pressure for human

heart.

Q (5*) Show that the centre of pressure for a vertical semi-circular plane submerged in a

homogeneous liquid and with its diameter d at the free surface lies on the centre line at a depth of

3d/32 from the free surface.

Q (6*) In the vertical end of an oil tank is a plane rectangular inspection door 600 mm wide and 400

mm deep which closely fits an aperture of the same size. The door can open about one vertical edge

by means of two hinges, respectively 125mm above and below the horizontal centre-line, and at the

centre of the opposite vertical edge is a locking lever. Determine the forces exerted on each hinge

and on the locking lever when the tank contains an oil of relative density 0.9 to a depth of 1m above

the centre of the door and the air above the oil surface is at a gauge pressure of 15 kPa.

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