Question

In the figure shown a liquid is flowing through a tube at the rate of 0.1 kg/sec. The tube is branched into two semi circular tubes of cross sectional area A/3 and 2A/3. The velocity of liquid at Q is (the cross-section of the main tube (1) = 10^-2 m² and v_p = 20 m/sec.)

• A. 5 m/s
• B. 30 m/s
• C. 35 m/s
• D. None of these.

Answer 1

Answer: (A)

5 m/s

Answer 2

Equation of continuity:

Rate = r = A/3 v_p + 2A/3v³

⇒ v_p + 2 v_Q = …(1)

⇒ v_p + 2v_Q = $\frac { 3 \times 0.1 } { 10 ^ { - 2 } }$ = 30 m/sec.

where v_p = 20 m/sec. ⇒ v_Q = 5 m/sec.

Therefore (1).