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JEE Main 20198 AprilMorning Shift
Exam
JEE Main
Year
2019
Date
8 April
Shift
Morning Shift
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Main 2019 · 8 April · Morning Shift · Physics · Mechanical Properties of Fluids

Water from a pipe is coming at a rate of 100 liters per minute. If...

Water from a pipe is coming at a rate of 100100 liters per minute. If the radius of the pipe is 5cm,5cm, the Reynolds number for the flow is of the order of: (density of water = 100kg/m3,100kg / {m}^{3}, coefficient of viscosity of water =1mPas)= 1mPas )

Options

  1. A102{10}^{2}
  2. B104{10}^{4}
  3. C103{10}^{3}
  4. D106{10}^{6}

Correct answer

B. 104{10}^{4}

Step-by-step solution

Volume flow rate =πr2v=100lmin⁡= \pi{r}^{2}v = 100\dfrac{l}\min
⇒πr2v=1600m3/sec⇒ \pi{r}^{2}v = \dfrac{1}{600}{m}^{3} / sec
⇒v=1600πr2m/sec⇒ v = \dfrac{1}{600\pi{r}^{2}}m / sec
Reynolds number Re=ρvDηRe = \dfrac{ρvD}{η}
=10001×10−3×1600πr2×2r= \dfrac{1000}{1 \times {10}^{- 3}} \times \dfrac{1}{600\pi{r}^{2}} \times 2r
=20000.6π(5×10−2)=21220.66=2.1×104= \dfrac{2000}{0.6\pi\left(5 \times {10}^{- 2}\right)} = 21220.66 = 2.1 \times {10}^{4}
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