Question

Air flows steadily along a streamline from point 1 to point 2 with negligible viscous effects. The following conditions are measured:

a) at point 1z1=2m and p1=0kPa
b) at point 2 z2=10m p2=20 N/m^2 and V2=0.
c) Determine the velocity at point 1.

Answer 1

The velocity at point 1 can be calculated using Bernoulli's principle, with the given height and pressure at points 1 and 2, assuming air density and gravity are known.

Step-by-step explanation:

The student's question involves applying Bernoulli's principle to determine the velocity at point 1 of a streamline where air flows from point 1 to point 2. Since air flows steadily with negligible viscous effects and the velocity at point 2 (V2) is 0, we can use Bernoulli's equation to find the velocity at point 1 (V1).

We have that at point 1, the pressure P1 is 0 Pa and the height z1 is 2 m, while at point 2, the pressure P2 is 20 N/m², the height z2 is 10 m, and the velocity V2 is 0 m/s. Considering the equation for Bernoulli's principle along a streamline:

P1 + ½ ρ V1² + ρ g z1 = P2 + ½ ρ V2² + ρ g z2

Since V2 = 0, we can rearrange the equation to solve for V1:

V1 = √[(2(g)(z2 - z1) + (2(P2 - P1)/ρ))]

Here, ρ is the density of the air and g is the acceleration due to gravity. Note that pressure is given in N/m² (Pascals), and ρ and g need to be in consistent units to calculate V1 accurately.