Answer
given,
Air speed, v = 20 m/s
Pressure gradient, = 105 N/m³
distance,dl = 0.5 m
density of air = 1.23 kg/m³
Airspeed at 0.5 m = ?
relation between pressure gradient and speed changed
[tex]-\frac{\partial p}{\partial l}-\gamma sin\theta = \rho_{air}v\frac{\partial v}{\partial l}[/tex]
neglecting the gravity
[tex]-\frac{\partial p}{\partial l}-0 = \rho_{air}v\frac{\partial v}{\partial l}[/tex]
[tex]-105= 1.23\times 20\times \frac{\partial v}{\partial l}[/tex]
[tex]\frac{\partial v}{\partial l} = -4.26[/tex]
[tex]\partial v = -4.26 \times \partial l[/tex]
[tex]\partial v = -4.26 \times 0.5[/tex]
[tex]\partial v = -2.13\ m/s[/tex]
Speed of the air at 0.5 m
V = 20 - 2.13
V = 17.87 m/s
Hence, the speed of air is equal to V = 17.87 m/s
