Question

Suppose you have a wind speed gauge like the pitot tube shown in Figure 12.7(b). By what factor must wind speed increase to double the value of hin the manometer? Is this independent of the moving fluid and the fluid in the manometer?

Answer 1

(a) By what factor must wind speed increase to double the value of hin the manometer?

$\Rightarrow$ Let v₁ be the initial wind speed and v₂ be the final wind speed.

Then, we have

v₁$\propto$_$\sqrt{}$h $\Leftrightarrow$ h $\propto$ v₁²                                              { eq.1 }

v₂$\propto$_$\sqrt{}$2h $\Leftrightarrow$ 2h $\propto$ v₂²                                          { eq.2 }

Dividing eq.2 by eq.1 & we get

(v₂² / v₁²) = [(2h) / (h)]

(v₂ / v₁) = _$\sqrt{}$2

(b) Is this independent of the moving fluid and the fluid in the manometer?

$\Rightarrow$ Yes, the wind speed factor is independent of the moving fluid and the fluid in the manometer.