Water flows in a horizontal tube (see figure). The pressure of water changes by $700 \text{ Nm}^{-2}$ between A and B where the area of cross section are $40 \text{ cm}^{2}$ and $20 \text{ cm}^{2}$, respectively. Find the rate of flow of water through the tube. (density of water $=1000 \text{ kg m}^{-3}$)

(C) $2720 \text{ cm}^{3}/\text{s}$

(A) $1810 \text{ cm}^{3}/\text{s}$

(B) $2420 \text{ cm}^{3}/\text{s}$

(D) $3020 \text{ cm}^{3}/\text{s}$

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Fluid Mechanics

Water flows in a horizontal tube (see figure). The pressure of water changes by

700 Nm^{- 2}

between A and B where the area of cross section are

40 cm^{2}

and

20 cm^{2}

, respectively. Find the rate of flow of water through the tube. (density of water

= 1000 kg m^{- 3}

)

Answer: (C)

Continuity fixes the two speeds:

A_{A} v_{A} = A_{B} v_{B}

with areas

40

and

20 cm^{2}

gives

v_{B} = 2 v_{A}

. Bernoulli's equation for the level tube,

P_{A} - P_{B} = \frac{1}{2} ρ (v_{B}^{2} - v_{A}^{2})

, then reads

700 = \frac{1}{2} (1000) (4 v_{A}^{2} - v_{A}^{2}) = 1500 v_{A}^{2}

, so

v_{A} = \frac{7}{15} m s^{- 1}

and

v_{B} = 2 \frac{7}{15} m s^{- 1}

. The volume flow rate is

Q = A_{B} v_{B} = 20 \times 1 0^{- 4} \times 2 \frac{7}{15} \approx 2.72 \times 1 0^{- 3} m^{3} s^{- 1}

, which is about

2720 c m^{3} s^{- 1}

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Single correct option