A beaker contains a fluid of density \rho kg/m3, specific heat S J/kg 0C and viscosity \eta. The beaker is filled up to height h. To estimate the rate of heat transfer per unit area (Q /A) by convection when beaker is put on a hot plate, a student proposes that it should depend on \eta,

\left ( \frac{S\Delta \Theta }{h} \right ) \: and\: \left ( \frac{1}{\rho g} \right )when \Delta \Theta   (in_{}^{0}\textrm{C}) is the  difference in the temperature between the bottom and top of the fluid. In that
situation the correct option for (Q /A) is:

 

  • Option 1)

    \eta \: \frac{S\Delta \Theta }{h}

  • Option 2)

    \eta \left ( \frac{S\Delta \Theta }{h} \right )\left ( \frac{1}{\rho \: g} \right )

  • Option 3)

    \frac{S\Delta \Theta}{\eta \: h}

  • Option 4)

    \left ( \frac{S\Delta \Theta }{\eta h} \right )\left ( \frac{1}{\rho \: g} \right )

 

Answers (1)

As we learnt in

Viscosity -

It is property of liquid due to which it opposes the relative motion between the layers

- wherein

Which is also known as fluid friction or internal friction

 

 It will be mgh because at all the points of a fluid are equal. 

\eta\frac{S\Delta \Theta}{h}

Correct option is 1.


Option 1)

\eta \: \frac{S\Delta \Theta }{h}

This is the correct option.

Option 2)

\eta \left ( \frac{S\Delta \Theta }{h} \right )\left ( \frac{1}{\rho \: g} \right )

This is an incorrect option.

Option 3)

\frac{S\Delta \Theta}{\eta \: h}

This is an incorrect option.

Option 4)

\left ( \frac{S\Delta \Theta }{\eta h} \right )\left ( \frac{1}{\rho \: g} \right )

This is an incorrect option.

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