Flow Measurement and Incompressible Flow
How can we determine the velocity of helium in a pipe using a Pitot-static tube and a water manometer reading?
Is it reasonable to consider the flow as incompressible?
Determining Helium Velocity and Consideration of Incompressible Flow
The velocity of helium in the pipe can be determined using the Pitot-static tube and the water manometer reading. To find the helium velocity, we can use Bernoulli's equation, which relates the pressure difference to the velocity of the fluid.
The flow can be considered as incompressible since the density of helium remains constant at the given conditions. This assumption allows us to use Bernoulli's equation and solve for the velocity of the helium using the Pitot-static tube and the water manometer reading.
Let's break down the steps to find the helium velocity:
- Determine the pressure difference:
- Calculate the velocity of helium:
- Solve for v (velocity of helium):
The water manometer reading indicates a reading of 0.06 m. We can convert this to a pressure difference by multiplying it with the density of water and the acceleration due to gravity.
Pressure difference = 0.06 m * 1000 kg/m³ * 9.8 m/s²
Using Bernoulli's equation, we can relate the pressure difference to the velocity of the helium.
Pressure difference = (1/2) * ρ * v², where ρ is the density of the fluid and v is the velocity of the fluid.
Rearranging the equation, we find v ≈ √((2 * 0.06 m * 1000 kg/m³ * 9.8 m/s²) / 0.1664 kg/m³) to calculate the velocity of helium.
In order to consider the flow as incompressible, the change in density of the fluid must be negligible. Helium, being a gas, behaves like an ideal gas at the specified conditions. Hence, we can assume that the density of helium remains constant during the flow measurement.