In the figure shown, a liquid is flowing through a tube at the rate of 0.1 $m^{3}$ /sec. The tube is randed into two semicircular tubes of cross sectional area $\frac{A}{3}$ and 2 $\frac{A}{3}$ . The velocity of liquid at Q is $V_{Q}$ and Velocity at P is $V_{P}$ (The cross-sectional area of the main is A)

If $V_{P}$ = 10 m/s, then $V_{Q}$ = 5 m/s

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If $V_{P}$ = 20 m/s, then $V_{Q}$ = 5 m/s

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If $V_{P}$ = 20 m/s, then $V_{Q}$ = 10 m/s

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If $V_{P}$ = 30 m/s, then $V_{Q}$ = 20 m/s

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Solution

The correct option is B
If $V_{P}$ = 20 m/s, then $V_{Q}$ = 5 m/s

Equation of continuity

Rate (r)= $\frac{A}{3} V_{p} + (A - \frac{A}{3}) V_{Q}$

$V_{P} + 2 V_{Q} = \frac{3 r}{A} = \frac{3 \times 0.1}{10^{- 2}} = 30 m / s$

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Similar questions

In the figure shown, a liquid is flowing through a tube at the rate of 0.1 $m^{3}$ /sec. The tube is randed into two semicircular tubes of cross sectional area $\frac{A}{3}$ and 2 $\frac{A}{3}$ . The velocity of liquid at Q is $V_{Q}$ and Velocity at P is $V_{P}$ (The cross-sectional area of the main is A)

Q. Figure 4.186 shows a liquid flowing through a tube at the rate of

0.1 m^{3} / s

. The tube is branched into semicircular tubes of cross-sectional area

A / 3

and

2 A / 3

. The velocity of liquid at

Q

is (the cross section of the main tube is

A = 10^{- 2} m^{2}

and

v_{p} = 20 m / s)

Q. Figure shows a liquid flowing through a tube at the rate of

0.1 m^{3} / s

. The tube is branched into two semicircular tubes of cross-sectional area A/3 (upper) and 2A/3 (lower). The velocity of liquid at Q is (the cross section of the main tube is

A = 10^{- 2} m^{2}

and

v_{P} = 20 m / s)

In the figure shown a liquid is flowing through a tube at the rate of 0.1 m³/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 (A) = 10^-2 m² and V_P = 20 m/sec.):