Question

Drive Bernoulli's theorum
?

Answer 1

Bernoulle's Theorem...

Proof

Consider a tune of area of cross section a1 and a2 with pressure P1 and P2 kept at a height h1 and h2 above the ground. The velocity of incoming liquid is v1 and out going liquid is v2 let w1 be the work done for incoming fluid and w2 be the work done for outgoing fliud.

W = F×S

w1= P1 × A1 × S1

w1= P1A1V1

w2= P2A2V2

w = w1 - w2

w = P1A1V1 - P2A2V2

w=P1m/d - P2m/d

w= (P1-P2)m/d _____eq. 1

KE1 = 1/2 mv1^2

KE2 = 1/2 mv2^2

==> 1/2 m ( v2^2-v1^2)______eq.2

PE1= mgh1

PE2= mgh2

PE= mg(h2-h1)____eq.3

The net work done is the sun of KE and PE.

(P1 –P2)m/d = 1/2 m (v2^2–v1^2) + mg(h2–h1)

P1-p2=1/2dv2^2 – 1/2dv1^2 + dgh2 – dgh1

P1+1/2dv1^2 + dgh1 = P2+ 1/2 dv2^2 + dgh2

P + 1/2 dv^2 + dgh = constant.....eq.3

Or

P/dg + 1/2 v^2/ g + h= constant.....