In a wind tunnel experiment, a team uses pitot tube to measure flow velocity, given the pressure difference equals 50 Pa, calculate the velocity. Assume p 1.16 kg/m a. 100.18 m/s b. 20.2 m/s c. 19.8 m/s d. 9.3 m/s

To calculate the flow velocity using the pressure difference in a pitot tube, you can use the Bernoulli's equation for incompressible flow. The pitot tube measures the stagnation pressure which is the sum of the static pressure and dynamic pressure. Dynamic pressure can be defined as:

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

where \( \rho \) is the density of the air (in kg/m^3) and \( v \) is the velocity of the flow (in m/s).

Given the pressure difference (which would be the dynamic pressure in this case) of 50 Pa (Pascals) and the air density (\( \rho \)) of 1.16 kg/m^3, we can solve for \( v \) using the formula:

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

Now we solve for \( v \):

\[ v = \sqrt{\frac{2 \cdot P_{dynamic}}{\rho}} \] \[ v = \sqrt{\frac{2 \cdot 50}{1.16}} \] \[ v = \sqrt{\frac{100}{1.16}} \] \[ v = \sqrt{86.2068966} \] \[ v ≈ 9.28 \]

So the flow velocity is approximately 9.3 m/s, which corresponds to option d.

Extra: In wind tunnel experiments, it is essential to measure the velocity of the airflow accurately to study aerodynamic forces acting on different models. The pitot tube is one of the simplest and most commonly used devices for this purpose.

Bernoulli's principle is the underlying principle for the pitot tube operation, which relates the speed of an incompressible fluid to the pressure within the fluid: as the speed of a fluid increases, the pressure within the fluid decreases, and vice versa.

It's important for students to note that the actual design of a pitot tube allows it to measure the stagnation pressure (the pressure at a stagnation point where the flow velocity is zero) as well as the static pressure (the ambient pressure of the fluid). The difference between these two pressures is the dynamic pressure, and it is from this value that the flow velocity is calculated as demonstrated in the answer. This measurement technique is widely used in various fields, including meteorology, aviation, and various branches of engineering.