Question

Water flows at a speed of $6cm{s}^{-1}$ 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?

Answer 1

Step 1: Given that:

The speed of water through tube(v) = $6cm{s}^{-1}$ = $6\times {10}^{-2}m{s}^{-1}$

Radius(r) of the tube = $\text{1cm}$ = ${10}^{-2}m$

Therefore the diameter of pipe(D) = 2r = $2\times {10}^{-2}m$

Coefficient of viscosity of water at room temperature($\eta$) = $\text{0.01 poise}$ = ${10}^{-2}poise$

In SI unit the value of $\eta$ = ${10}^{-2}\times 0.1decapoise={10}^{-3}daP$

Step 2: Formula and concept used:

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

$v=\frac{R\eta }{\text{ρ}D}$

$R=\frac{v\text{ρ}D}{\eta }$

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) = ${10}^{3}kg{m}^{-3}$

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

$R=(6\times {10}^{-2}m{s}^{-1})\times \frac{{10}^{3}kg{m}^{-3}\times (2\times {10}^{-2}m)}{{10}^{-3}daP}$

$R=12\times {10}^{-2+3-2+3}$

$R=12\times {10}^2$

$R=12\times 100$

$R=1200$

Since;

$0<1200<2000$

the flow is steady.

Hence,

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