As shown in figure, a liquid of density rho is standing in sealed container to a height h. The container contains compressed air at a gauge pressure of p.The horizontal outlet pipe has a cross-sectional area A at C and D. The cross-sectional area is A//2 at E. Find correct options:

As shown in figure, a liquid of density rho is standing in sealed co

1.	As shown in figure, a liquid of density rho is standing in sealed container to a height h. The container contains compressed air at a gauge pressure of p.The horizontal outlet pipe has a cross-sectional area A at C and D. The cross-sectional area is A//2 at E. Find correct options:
Answer» The velocity of liquid at C will be `[((P+rhogh))/(4rho)]^(1//2)` The velocity of liquid at C will be `[(2(P+rhogh))/(rho)]^(1//2)` the discharge rate is GIVEN by `(A)/(2RHO)(p+rhogh)^(1//2)` The discharge rate is given by `(A)/(2sqrt(rho))(p+rhogh)^(1//2)` Solution :`p_(A)=p+p_(0)+rhogh`. (1) Apply BERNOULLI's theorem at A and C and E `(p+p_(0))+rhogh=p_(c)+rho(V_(c)^(2))/(2)` `=p_(0)+rho(V_(E)^(2))/(2)`….(2) `=p_(c)+p_(0)+rhogh_(1)`.(3) `A_(C)V_(C)=A_(E)V_(E),A_(C)V_(C)=((A_(C))/(2))V_(E)`.(4) from eq. (2) `(p_(0)+rhogh_(1))+rho(V_(C)^(2))/(2)=p_(0)+rho(2V_(C))^(2)` or `h_(1)=(7V_(C)^(2))/(2g)` for eq. (2), `(p+p_(0))+rhogh=(p_(0)+rhogh_(1))+rho(V_(C)^(2))/(2)` `p+rhogh=rhog((7V_(C)^(2))/(2g))+(rhoV_(C)^(2))/(2),V_(C)^(2)=((p+rhogh))/(4rho)` Discharge rate `=A_(C)V_(C)=A(((p+rhogh))/(4rho))^(1//2)`