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    Mechanical Properties of Fluids
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    A vertical off-shore structure is built to withstand a maximum stress of 109 Pa. Is the structure suitable for putting up on top of an oil well in the ocean? Take the depth of the ocean to be roughly 3 km, and ignore ocean currents.
    The maximum allowable stress for the structure, P = 109 Pa

    Depth of the ocean, d = 3 km = 3 × 103 m

    Density of water, ρ = 103 kg/m3 

    Acceleration due to gravity, g = 9.8 m/s2 

    The pressure exerted because of the sea water at depth, d = ρdg 

                                                                               = 3 × 103 × 103 × 9.8 

                                                                               = 2.94 × 107 Pa 

    The maximum allowable stress for the structure (109 Pa) is greater than the pressure of the sea water (2.94 × 107 Pa).

    The pressure exerted by the ocean is less than the pressure that the structure can withstand.

    Hence, the structure is suitable for putting up on top of an oil well in the ocean.
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    Explain why:
    (e) A spinning cricket ball in air does not follow a parabolic trajectory.

    A spinning cricket ball has two simultaneous motions types of motion- rotatory and linear.
    These two types of motion oppose the effect of each other. This decreases the velocity of air flowing below the ball. Hence, the pressure on the upper side of the ball becomes lesser than that on the lower side. An upward force acts upon the ball. Therefore, the ball takes a curved path. Therefore, the ball does not follow a parabolic path. 

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    A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000
    kg. The area of cross-section of the piston carrying the load is 425 cm2. What
    maximum pressure would the smaller piston have to bear ?
    The maximum mass of a car that can be lifted, m = 3000 kg

    Area of cross-section of the load-carrying piston, A = 425 cm2 = 425 × 10–4 m2

    The maximum force exerted by the load, F = mg 

                                                            = 3000 × 9.8

                                                            = 29400 N 

    The maximum pressure exerted on the load-carrying piston, P = F/A

                                                                                    =fraction numerator 29400 over denominator 425 cross times 10 to the power of negative 4 end exponent end fraction

                                                                                    = 6.917 × 105 Pa 

    Pressure is transmitted equally in all directions in a liquid.

    Therefore, the maximum pressure that the smaller piston would have to bear is 6.917 × 10    5 Pa.
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    Torricelli’s barometer used mercury. Pascal duplicated it using French wine of density 984 kg/m3. Determine the height of wine column for normal atmospheric pressure.

    According to Pascal law, the
    According to Pascal law, the
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    A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other. What is the specific gravity of spirit? 
    Height of the spirit column, h1 = 12.5 cm = 0.125 m

    Height of the water column, h2 = 10 cm = 0.1 m

    P0 = Atmospheric pressure,
    ρ1 = Density of spirit,
    ρ2 = Density of water,

    Pressure at point B = P0 + ρ1h1g

    Pressure at point D = P0 + ρ2h2g

    Pressure at points B and D is the same. 

                                 P0 + ρ1h1g  =  P0 + ρ2h2g

                                      ρ1 / ρ2  =  h2 / h1 

                                   10 / 12.5  =  0.8 

    Therefore, the specific gravity of spirit is 0.8.
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