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8.11 Application of Bernoulli's principle

(i) The action of aspirator, carburetor, paint-gun, scent spray or is based on Bernoulli's principle.

In all these, by means of motion of a piston of a cylinder high air is passed over a tube dipped in liquid to be sprayed. High speed air creates low pressure over the tube due to which liquid rises in it and is then blown off in very small droplets with expelled air.

(ii) Velocity of efflux

(a) The speed of liquid coming out of orifice is independent of the nature and quantity of liquid in the container or the area of the orifice.

(b) Greater is the distance of the hole from the free surface of liquid, greater will be velocity of efflux (i.e. physics problems). This is the reason that liquid flows out with maximum velocity from the orifice which is at maximum distance from the free surface of the liquid.

(c) As the vertical velocity of liquid at the orifice is zero and it is at a height (H - h) from the base, the time taken by the liquid to reach the base-level.

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(d) Range of liquid flowing out from the orifice is

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This range will be maximum (= H) when h = H/2

(e) Range will be same if the orifice is at a depth h or (H – h) below the free surface or range is same for liquid coming out of holes at same distance below and above the bottom.

(f) If the hole is at the bottom of the tank, time t taken by the tank to be emptied.

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where A0 is the area of orifice or hole and A that of container.

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