Question

three ruvers R1,R2,R3 merge together to form river R4.the cross sectional areas of three rivers R1,R2&R3 are in yhe ratio 1:2:3& speed of water flowing in these are in ratio 1:1\2:1\3.assuming streamline flow ,if R4 has cross sectional area equal to that of R1 ,the ratio of speed of water in R4 to ghat in R1 is?

Answer 1

discharge= velocity * cross section area
R1 :R2 :R3 =area=1:2:3
R1=1x, R2=2x, R3=3x cross section areas
and velocities 1:1/2:1/3=>6:3:2
R1=6y, R2=3y, R3=2y
R1 discharge = 1x*6y =6xy
R2. " =6xy
R3. = 6xy
R4 discharge=R1+R2+R3 = 18xy
R4 has same cross section as R1= 1x
so,R4 has velocity =18y
R4:R3(velocity ratio)=18y:6y
=3:1