If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter\frac{2}{\sqrt{\pi }} cm  then the Reynolds number for the flow is (density of water =103 kg/m3 and viscosity of water10-3 Pa.s) close to :

  • Option 1)

    5500

  • Option 2)

    11,000

  • Option 3)

    550

  • Option 4)

    1100

 

Answers (1)

As we learnt in

Range of Reynold's number -

Between 0 - 2000 \rightarrow streamline or laminar

2000 - 3000 \rightarrow unstable liquid (streamline to turbulent)

Above - 3000\rightarrow turbulent

-

 

 

Viscosity -

It is property of liquid due to which it opposes the relative motion between the layers

- wherein

Which is also known as fluid friction or internal friction

 

 We know that 

Reynold's number R=\frac{\rho vd}{\eta}

The volume of the water flowing out per second.

Q=v\times\frac{\pi d^{2}}{y}\ \; \Rightarrow\ \; Y=\frac{4Q}{d^{2}\pi}

R=\frac{\rho vd}{\eta}\ \Rightarrow\ \; \frac{\rho Q4}{\pi d \eta}

\rho = Density of water  \rho =10^{3} kg/m^{3}

Q = \frac{3L}{min}=\frac{3\times 10^{-3}}{60}=5\times 10^{-5}m^{3}/sec

d=\frac{2}{\sqrt{\pi}}\times10^{-2}mt = 1.125\times10^{-2}m^{3}/sec

\eta=Viscosity=10^{-3}Pa-s

\therefore\ \;R=\frac{4\times10^{3}\times5\times10^{-5}}{3.14\times1.125\times10^{-2}\times10^{-3}}

\therefore\ \;R\simeq5500

Correct option is 1.    


Option 1)

5500

This is the correct option.

Option 2)

11,000

This is an incorrect option.

Option 3)

550

This is an incorrect option.

Option 4)

1100

This is an incorrect option.

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