Question

State and explain bernoulli's theorem write the construction, working

Answer 1

Answer:

According to Bernoulli's theorm the sum of pressure energy, potential energy and kinetic energy per unit volume during streamlined flow is remains constant.

Explanation:proof:

Work done on the liquid X=FxD= p1A1V1

Work done by the liquid Y= P2a2v2

Net work done= p1a1v1 - p2a2v2

If the mass of the liquid flowing per second =m

Then the increase in K. E =1/2 (mv2)2- 1/2 (mv1)2

Increase in P. E= mgh2-mgh1

According to conservation law of energy

Net work done =increase in K. E + increase in P. E

P1a1v1-p2a2v2 = 1/2(mv2)2-1/2(mv1)2+mgh2-mgh1

P1a1v1+ 1/2(mv1)2+mgh1=p2a2v2 + 1/2(mv2)2+mgh2

P1v+1/2(mv1)2+mgh1=p2v+1/2(mv2)2+mgh2 (a1=a2=v ) (acc.to liquid flow in one second)

Dividing whole equation by volume

P1v/v+ 1/2(mv1)2/v+mgh1/v= p2v/v+ 1/2(mv2)2/v+mgh2/v

P1+1/2ro(v1)2 +rogh=p2+1/2ro(v2)2+rogh

P+1/2ro V2+rogh= constant