Question

Can you calculate the Reynolds number and determine the flow type? Calculate the Reynolds number for the flow of water in each case. The flow rate through the hose and nozzle is 0.01 L/s. The density of water is 1000 kg/m3 and the viscosity of water is 8.9 × 10-4 Pa·s. (a) Through a nozzle with a radius of 0.250 cm.

Answer 1

Answer:

The Reynolds number is $2.86\times10^{3}$ and flow is transition.

Explanation:

Given that,

Flow rate = 0.01 L/s

Density of water = 1000 kg/m³

Viscosity of water $\eta=8.9\times10^{-4}\ Pa-s$

Radius = 0.250 cm

We need to calculate the Reynolds number

Using formula of Reynolds number

$N_{R}=\dfrac{2\rho\times v\times r}{\eta}$

$N_{R}=\dfrac{2\rho\times\dfrac{Q}{A}\times r}{\eta}$

Where, $\rho$ = water density

$\eta$ = viscosity of water

Q = flow rate

A = area

r = radius

v = velocity

Put the value into the formula

$N_{R}=\dfrac{2\times1000\times\dfrac{0.01\times10^{-3}}{\pi\times(0.250\times10^{-2})^2}\times0.250\times10^{-2}}{8.9\times10^{-4}}$

$N_{R}=2.86\times10^{3}$

Reynolds number is below 2,000 then the flow is laminar and when it is above 4,000, then the flow will be turbulent. When the Reynolds number lies between these two limits, then the flow is transition flow.

Hence, The Reynolds number is $2.86\times10^{3}$ and flow is transition.