Question

The flow rate of water from a tap of diameter $1.25\,cm$ is $3\,L\,per\,\min $. The coefficient of viscosity of water is ${10^{ - 3}}\,Pa\,s$. The nature of flow is
A. Unsteady
B. Turbulent
C. Laminar
D. None of these

Answer 1

Hint:Here, in the question, we are given a water of viscosity is ${10^{ - 3}}\,Pa\,s$. Here, we will calculate the Reynolds number to find out the nature of the flow of the water. If the Reynolds number is less than $2000$, then the flow of water will be laminar. On the other hand, if the Reynolds number is greater than $2000$, then the flow of water will be turbulent.

Formula used:
The formula of Reynolds number used to find the nature of flow is given below
${R_e} = \dfrac{{4\rho Q}}{{\pi D\eta }}$
Here, ${R_e}$ is the Reynolds number, $\rho $ is the density of the fluid, $Q$ is the volume of the fluid flowing out per second, $D$ of the object through which the fluid will flow and $\eta $ is the coefficient of viscosity of the fluid.

Complete step by step answer:
The terms given below are given in the question
The diameter of the tap, $D = 1.25\,cm = 1.25 \times {10^{ - 2}}m$
Density of the water, $\rho = {10^3}kg{m^{ - 3}}$
Coefficient of viscosity of the flow, $\eta = {10^{ - 3}}\,Pa\,s$
Now, the volume of the water flowing out per second is given below
$Q = 3L\,per\,\min $
$ \Rightarrow \,Q = \dfrac{{3 \times {{10}^{ - 3}}\,{m^3}}}{{60\,s}}$
$ \Rightarrow \,Q = 5 \times {10^{ - 5}}\,{m^3}\,{s^{ - 1}}$
Now, the nature of the flow can be calculated by using the formula of the Reynolds number which is given below
${R_e} = \dfrac{{4\rho Q}}{{\pi D\eta }}$
$ \Rightarrow \,{R_e} = \dfrac{{4 \times {{10}^3}kg\,{m^{ - 3}} \times 5 \times {{10}^{ - 5}}{m^3}\,{s^{ - 1}}}}{{3.14 \times 1.25 \times {{10}^{ - 2}}m \times {{10}^{ - 3}}\,Pa\,s}}$
$ \therefore \,{R_e} = 5095$
Now, we can see that the value of the Reynolds number is greater than $2000$. This is the condition of turbulence flow of liquid. Therefore, the flow of the water is turbulent in nature.

Hence, option B is the correct answer.

Note:For solving these types of questions, we must first convert the larger units into smaller units. Here, the volume of the liquid is given in liters that is why we have converted it in meters. Also, the flow will not be unsteady because the unsteady flow depends on time and we don’t have the value of time in the question.