Answer

Verified

436.5k+ views

**Hint:**In given numerical rate of water flow, coefficient of viscosity length of pipe and pressure difference is given at fixed temperature. Using poiseuille’s law and on substituting the values of all these physical quantities we get a radius of pipe.

**Formula used:**

According to poiseuille’s law, the rate of flow of water is given as

$Q = \dfrac{{\Delta \rho \pi {r^4}}}{{8\eta \ell }}$

Where

$\Delta \rho = $ Pressure difference

r $ = $ Radius of pipe

$\eta = $ Coefficient of viscosity

$\ell = $ Length of pipe

**Complete step by step answer:**

Given that

Pressure difference $\Delta \rho = 60kPa$

$\Delta \rho = 60 \times {10^{ - 3}}Pa$

Coefficient of viscosity $\eta = {10^{ - 3}}$

Length of pipe $\ell = 100m$

Rate of water flow $Q = \dfrac{{3 \times {{10}^{ - 3}}}}{{60}}$

$Q = 5 \times {10^{ - 5}}{m^3}{s^{ - 1}}$

According to poiseuille’s law, the rate of flow of water is given by

$\Rightarrow Q = \dfrac{{\Delta \rho \pi {r^4}}}{{8\eta \ell }}$

$\Rightarrow {r^4} = \dfrac{{8Q\eta \ell }}{{\Delta \rho \pi }}$ $[\because \pi = 3.14]$

On putting all the values in above expression

$\Rightarrow {r^4} = \dfrac{{8 \times 5 \times {{10}^{ - 5}} \times {{10}^{ - 3}} \times 100}}{{60 \times {{10}^3} \times 3.14}}$

$\Rightarrow {r^4} = \dfrac{{40 \times 100 \times {{10}^{ - 8}}}}{{188.4 \times {{10}^3}}}$

$\Rightarrow {r^4} = \dfrac{{4000}}{{1884}} \times {10^{ - 8}} \times {10^{ - 2}}$

$\Rightarrow {r^4} = 2.12 \times {10^{ - 10}}$

$\Rightarrow {r^2} = \sqrt {2.12 \times {{10}^{ - 10}}} $

$\Rightarrow {r^2} = 1.457 \times {10^{ - 5}}$

$\Rightarrow r = \sqrt {1.457 \times {{10}^{ - 5}}} $

$\Rightarrow r = \sqrt {14.57 \times {{10}^{ - 6}}} $

$\Rightarrow r = 3.187 \times {10^{ - 3}}m$

$\Rightarrow r \approx 3.82 \times {10^{ - 3}}m$

$\Rightarrow r \approx 3.82 \times {10^{ - 1}}cm$

$\therefore r \approx 0.38cm$

**Hence, the radius of pipe is $0.38 cm$. So, option B is the correct answer.**

**Note:**Many times students may get confused between dynamic viscosity and kinematic viscosity.Dynamic viscosity is the measurement of the fluid’s internal resistance to flow.Kinematic viscosity if the ratio of dynamic viscosity to density.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which are the Top 10 Largest Countries of the World?

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE