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Given that an ideal fluid flows in the tube as shown figure.
The pressure of the fluid at the bottom (P_2)(P2) is equal to the pressure of the fluid at the top (P_1)(P1) i.e. (P_1=P_2)(P1=P2) )
The difference in height of the top and bottom h_1-h_2=3mh1−h2=3m
The velocity of the fluid at the top v_1=2m"/"sv1=2m/s
The velocity of the fluid at the bottom v_2="unknown"v2=unknown
The area of cross-section of the pipe at the top A_1A1
The area of cross-section of the pipe at the bottom A_2A2
We are to find out the ratio of A_1:A_2A1:A2
Now applying Bernoulli principle
"Energy per unit volume at the top"= "Energy per unit volume at the bottom"Energy per unit volume at the top=Energy per unit volume at the bottom
we have the following equation
P_1+1/2rhov_1^2+rhogh_1=P_2+1/2rhov_2^2+rhogh_2P1+12ρv21+ρgh1=P2+12ρv22+ρgh2
where
rho= "density of the fluid"ρ=density of the fluid
and g = "acceleration due to pop gravity"=10m"/"s^2 andg=acceleration due to pop gravity=10m/s2
Inserting given values in the above equation we get
cancelP_2+1/2cancelrho2^2+cancelrho10h_1=cancelP_2+1/2cancelrhov_2^2+cancelrho10h_2
=>2+10h_1=1/2v_2^2+10h_2
=>2+10h_1-10h_2=1/2v_2^2
=>2+10(h_1-h_2)=1/2v_2^2
=>2+10xx3=1/2v_2^2
=>v_2^2=64
=>v_2=sqrt64=8m"/"s
Now applying principle of continuity of flow of ideal fluid we can write
A_1/A_2=v_2/v_1=(8m"/"s)/(2m"/"s)=4/1 which is option (2)
