Question

The wind velocity at a height of 2m above the ground is 15 km/hr. The velocity at a height of 10 m above the ground will be

Answer 1

Answer:

18.877 km/hr

Explanation:

For height about 500 m above the ground level, the wind velocity can be assumed to follow 1/7 power law and can be given by formula:

$v=Ch^{1/7}$

where v=wind velocity at height h above the ground

C=constant and h=given height

therefore, from the given question

$15=C*2^{1/7}$                                                 equation(1)

and let velocity above 10m height be x, then:

$x=C*10^{1/7}$                                                equation(2)

dividing equation(1) by equation(2),we get

$\frac{15}{x}=(\frac{2}{10} )^{1/7} \\\\\frac{15}{x}=(\frac{1}{5} )^{1/7} \\x=15*5^{1/7}$

On solving:

x=18.877 km/hr.

Answer 2

Answer:

The wind velocity at height 10m above the ground will be equal to 18.877km/hr.

Explanation:

Given: The height above the ground level, $h=2m$

At height h, the wind velocity $v=15km/hr$

Assume that the wind velocity follows 1/7th power law:

∴  $v=Ch^{\frac{1}{7} }$

where v is wind velocity, C is constant  and h is height

Therefore, $15=C*2^{\frac{1}{7} }$                                         .......................(1)

Now, assume that at height 10m , the wind velocity will be x,

$x=C*10^{\frac{1}{7} }$                                                           ......................(2)

By dividing eq.(2) by eq.(1),

$\frac{x}{15}=\frac{C*10^{\frac{1}{7} }}{C*2^{\frac{1}{7} }}$

$x=15*(\frac{10}{2} )^{\frac{1}{7} }$

$x=15*5^{\frac{1}{7}}\\x=18.877kmhr^{-1}$

Therefore, the velocity at a height of 10 m above ground is 18.87km/hr.