Laws of Motion Test - 2

In the experiment it is found that the mercury column in the barometer has a height of about 76 cm at sea level equivalent to one atmosphere (1 atm). This can also be obtained using the value of P; given by ρgh. A common way of stating pressure is in terms of cm or mm of mercury (Hg). A pressure equivalent of 1 mm is called a torr (after Torricelli)

According to the expression to obtain the pressure at a depth h,

ρgh = 1.29 kg m^-3 × 9.8 m s² × (h) m = 1.01 × 105 Pa

∴ h = 7989 m ≈ 8 km

Here h = 1000 m and ρ = 1.03 × 10³ kg m^­-3.

Gauge pressure is P – P_a = ρgh = P_g = 1.03 × 10³ kg m^­-3 × 10 ms^-2 × 1000 m = 103 × 10⁵ Pa ≈ 103 atm.

Now the force exerted on the window of the submarine

The pressure outside the submarine is P = Pa + ρgh and the pressure inside it is Pa. Hence, the net pressure acting on the window is gauge pressure, P_g = ρgh. Since the area of the window is A = 0.04 m², the force acting on it is F = PgA = 103 × 10⁵ Pa × 0.04 m² = 4.12 × 10⁵ N.

Whenever external pressure is applied on any part of a fluid contained in a vessel, it is transmitted undiminished and equally in all directions. This is the Pascal’s law for transmission of fluid pressure and has many applications in daily life. A number of devices such as hydraulic lift and hydraulic brakes are based on the Pascal’s law.

Here the depth of the lake from the water surface is, h = 10 m and ρ = 1000 kg m^-3.

Take g = 10 m s^-2

As we know the pressure at the bottom is given as,

P = Pa + ρgh = 1.01 × 10⁵ + 1000 × 10 × 10 = 2.01 × 10⁵ Pa ≈ 2 atm

The pressure P, at depth below the surface of a liquid open to the atmosphere is greater than atmospheric pressure by an amount ρgh. The excess of pressure, P −Pa, at depth h is called a gauge pressure at that point.

Atmospheric pressure, sometimes also called barometric pressure (after the sensor), is the pressure within the atmosphere of Earth. The standard atmosphere (symbol: atm) is a unit of pressure defined as 1,013.25 mbar (101,325 Pa), equivalent to 760 mm Hg or 760 torr