Question

At a given location the airspeed is 22 m/s and the pressure gradient along the streamline is 105 N/m3. Estimate the airspeed at a point 0.5 m farther along the streamline. First write the equation for the pressure gradient along the streamline. If neglest gravity,

Answer 1

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

$-\frac{\partial p}{\partial l}-\gamma sin\theta = \rho_{air}v\frac{\partial v}{\partial l}$

neglecting the gravity

$-\frac{\partial p}{\partial l}-0 = \rho_{air}v\frac{\partial v}{\partial l}$

$-105= 1.23\times 20\times \frac{\partial v}{\partial l}$

$\frac{\partial v}{\partial l} = -4.26$

$\partial v = -4.26 \times \partial l$

$\partial v = -4.26 \times 0.5$

$\partial v = -2.13\ m/s$

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