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Question

Water flows at a speed of 6cms1 through a tube of radius 1 cm. Coefficient of viscosity of water at room temperature is 0.01 poise. Calculate the Reynolds number. Is it a steady flow?

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Solution

Step 1: Given that:

The speed of water through tube(v) = 6cms1 = 6×102ms1

Radius(r) of the tube = 1cm = 102m

Therefore the diameter of pipe(D) = 2r = 2×102m

Coefficient of viscosity of water at room temperature(η) = 0.01 poise = 102poise

In SI unit the value of η = 102×0.1decapoise=103daP

Step 2: Formula and concept used:

The relation between the coefficient of viscosity and the speed of a fluid is given by;

v=RηρD

R=vρDη

Where, v = Speed of fluid

R = Reynold's number

ρ= Density of fluid

D = Diameter of the tube through which fluid is flowing

The density of water(ρ) = 103kgm3

If the value of Reynold's number lies between 0 to 2000, the flow of fluid is steady.

Step 3: Calculation of Reynold's number:

Using the formula for Reynold's number and putting the values we get

R=(6×102ms1)×103kgm3×(2×102m)103daP

R=12×102+32+3

R=12×102

R=12×100

R=1200

Since;

0<1200<2000

the flow is steady.

Hence,

The value of Reynold's number is 1200 and the flow is steady.


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