Question

A 1.0-cm-diameter pipe widens to 2.0 cm, then narrows to 0.5 cm. Liquid flows through the first segment at a speed of 9.0 m/s .

What is the speed in the second segment?

What is the speed in the third segment?

What is the volume flow rate through the pipe?

for the love of god please give me the right answer. everyone has given me the wrong answers so far and i'm pissed off.

Answer 1

Diameters d = 1 cm

              d ' = 2 cm

              d " = 0.5 cm

Speed through first segment v = 9 m/s

Speed through second segment v ' = ?

Speed thriugh third segment v " = ?

From equation of continuity Av = A ' v '

d ² v = d ' ² v '             Since A = (pi)d ² / 4

     v ' = v (d /d ') ²

        = 9 (1/2) ²

       = 2.25 m/s

From equation of continuity Av = A " v "

d ² v = d " ² v "             Since A = (pi)d ² / 4

     v " = v (d /d ") ²

        = 9 (1/0.5) ²

       = 36 m/s

the volume flow rate through the pipe = Av

                                                     = [ (pi)d ² / 4] v

                                                     = [3.1415 (0.01) ²/ 4 ] (9)       Since d = 1 cm = 0.01 m

                                                     = 7.068x10 ^-4 m ³/ s