Question

At a given location the airspeed is 20 m/s and the pressure gradient along the streamline is 100 N/m3. Estimate the airspeed at a point 0.5 m farther along the streamline.

Answer 1

Answer:

17.97m/s

Explanation:

Density of air (ρ)air=1.23 kg/m3, and

Air speed (V) =20 m/sec, pressure gradient along the streamline, ∂p/∂x = 100N/m^3.

The equation of motion along the stream line directions:

considering the momentum balance along the streamline.

γsinθ-∂p/∂x=ρV(∂V/∂x)

Neglecting the effect of gravity , then γ=ρg=0

So, ∂p/∂x= -ρV(∂V/∂x)

∂V/∂x= - 100/(20X1.23)= -4.0650407/S

Also δV/δx=∂V/∂x

∂V/∂x=-4.0650407/S and δx=0.5 m

δV = (-4.0650407/S) *(0.5m)

δV = -2.0325203 m/S

So net air speed will be V+δV= -2.0325203+20 ≅17.96748 m/s

Approximately, V+δV=17.97m/s.