Question

In a wind tunnel a flow is sped up. In the reservoir, the velocity is approximately zero; in the test section, the air is at standard conditions with a flow speed of 30 m/s.

What is the total pressure in the test section?

unanswered

What is the static pressure in the reservoir?

Answer 1

To determine the total pressure in the test section of the wind tunnel, we can use the Bernoulli equation. The total pressure \( P_t \) is defined as the sum of the static pressure \( P \) and the dynamic pressure \( q \):

\[
P_t = P + q
\]

where dynamic pressure \( q \) is given by:

\[
q = \frac{1}{2} \rho v^2
\]

In standard conditions (approximately sea level), the density of air \( \rho \) is about \( 1.225 \, \text{kg/m}^3 \) and the flow velocity \( v \) in the test section is given as \( 30 \, \text{m/s} \).

### Step 1: Calculate the dynamic pressure

Using the formula for dynamic pressure:

\[
q = \frac{1}{2} \rho v^2 = \frac{1}{2} (1.225) (30)^2
\]

Calculating this step-by-step:

1. Calculate \( v^2 \):
\[
(30)^2 = 900 \, \text{m}^2/\text{s}^2
\]

2. Now substitute:
\[
q = \frac{1}{2} (1.225) (900) = 0.6125 \times 900 = 551.25 \, \text{Pa}
\]

### Step 2: Determine static pressure in the test section

At standard atmospheric conditions, the static pressure \( P \) is approximately \( 101325 \, \text{Pa} \) or \( 101.325 \, \text{kPa} \).

### Step 3: Calculate total pressure in the test section

Now we can substitute our values into the formula for total pressure:

\[
P_t = P + q = 101325 \, \text{Pa} + 551.25 \, \text{Pa} = 101876.25 \, \text{Pa}
\]

### Final Answer for Total Pressure in Test Section

The total pressure in the test section is approximately:

\[
P_t \approx 101876.25 \, \text{Pa} \quad (\text{or } \approx 101.88 \, \text{kPa})
\]

### Regarding the Static Pressure in Reservoir

In the wind tunnel's reservoir, if we assume the flow velocity is effectively zero (as stated), and that it is at the same temperature and density, we can consider the static pressure in the reservoir to be the same as the standard atmospheric pressure:

\[
P \approx 101325 \, \text{Pa}
\]

### Summary of Answers:
- Total Pressure in the Test Section: \( 101876.25 \, \text{Pa} \) (or \( \approx 101.88 \, \text{kPa} \))
- Static Pressure in the Reservoir: \( 101325 \, \text{Pa} \) (or \( 101.325 \, \text{kPa} \))