Question

Three Rivers R1,R2,R3 merge together to form a river,R4. The cross sectional areas of the three Rivers R1,R2,R3 are in ratio 1:2:3 and speed of the water flowing in these are in the 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 that in R1 is (a) 4:1 (b) 3:1 (c)2:1

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=2yR1 discharge = 1x*6y =6xyR2. " =6xyR3. = 6xyR4 discharge=R1+R2+R3 = 18xyR4 has same cross section as R1= 1xso,R4 has velocity =18yR4:R3(velocity ratio)=18y:6y=3:1