Ac cording to Bernoulli's theorem for the streamline flow of an ideal liquid, the sum of pressure energy/mass, kinetic energy/mass and potential energy /mass remains constant at every cross section, throughout the liquid flow. i.e., `(P)/(rho) + (1)/(2)upsilon^2 + gh` = cosntant, where the symbols have their usual meaning. Note that an ideal liquied is the one, which is perfectly incompressible, irrotational and non visous. Read the above passage and answer the following question ? (i) At what speed will the velocity head of a stream of water be equal to 40 cm ? (ii) What is the implication of Bernoulli's theorem in day to day life ?

Explanation

(i) Velocity head, `(upsilon^2)/(2g) = 40 cm`
`upsilon = sqrt(2g xx 40) = sqrt(2xx980 xx 40) = 280 cm`
(ii) Bernoulli's theorem shows that at any cross section of liquid in motion, if velocity is more, pressure is less and vice - versa. It means you can increase one at the cost of the other. The same is true in day to day life. You have to sacrifice something to acquire another. You can decided your priorites as to what you want and what not.