Question

6. Water from a pipe is coming at a rate of 100 liters
per minute. If the radius of the pipe is 5 cm, the
Reynolds number for the flow is of the order of
(density of water = 1000 kg m , coefficient of
viscosity of water = 1 mPa s.)
(b) 104
(d) 106 (JEE Main 2019)
(a) 102
(c) 103​

Answer 1

answer of this is very very easy as we know that the answer is 106

Answer 2

Reynolds number for the flow is of the order of 10⁴

Therefore, Option (b) is correct

Explanation:

Discharge of water Q = 100 litres/min

                                    = 0.1/60 m³/s

Radius of the pipe r = 5 cm = 0.05 m

Cross sectional area of the pipe A = πr² = 3.14×(0.05)²

Thus, the velocity of flow

v = Q/A

$\implies v=\frac{0.1}{60\times 3.14\times 25\times 10^{-4}}$

$\implies v=0.21$ m/s

Reynold's number is given by

$R_e=\frac{\rho vd}{\eta}$

$\implies R_e=\frac{1000\times 0.21\times 10\times 10^{-2}}{10^{-3}}$

$\implies R_e=2.1\times 10^4$

or we can say that the flow is of the order 10^4

Hope this answer is helpful.

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