EFPLAB1: Venturi

Volume flow rate: l/s

Real case (friction & height changes considered)

Friction considered / height changes neglected

Friction neglected / height changes considered

Ideal case (friction & height changes neglected)

$$ p_{rel}= p_{hydro}= \rho \cdot g \cdot \Delta h = \rho \cdot g \cdot ( h - h_{ref}) $$

$$ \it{v= \frac{\dot{\mathbf{V}}}{A} }$$

Pressure curves explanation:

The red curve shows the pressure difference Δp between the calculated curve of the case "friction neglected/ height changes considered" p_{NoFrictionWithHeight} and the measured static pressure curve "Real case" p_real. The pressure difference Δp is also visible in the static pressure diagram as the area between the corresponding pressures if switched on.

$$ \Delta p= p_{NoFrictionWithHeight}- p_{real} $$

Pressure Losses occur due to friction in and on the fluid, generating frictional heat. The losses are irreversible, i.e. the frictional heat can no longer be converted into kinetic, potential and/or pressure energy. Thus, due to the irreversibility, the pressure loss curve along the current path must be constantly increasing. Consequently, the pressure difference curve Δp cannot be justified solely by the pressure loss, since the pressure difference curve decreases in the range of measuring positions 8 to 10.

The decreasing pressure difference is related to the simplifying assumption that there is a uniform velocity distribution in each cross-section. (Prerequisite to apply Bernoulli's equation along a representative flow path). However, the velocity profiles that actually occur (see figure) are non-uniform. The non-uniform velocity distribution has the consequence that the kinetic energy portion of the flow becomes larger. Since the kinetic energy depends on the velocity squared, the locally higher velocities are weighted more heavily. Consequently, the decrease in the pressure difference Δp in the range MP 8 to 10 can be explained by the velocity distribution becoming more uniform again and the associated decrease in the kinetic energy or the increasing pressure energy.

The approximated pressure drop p_L is continuously increasing and is proportional to the square of the velocity for turbulent flows.

$$ p_{V} \sim v^2 $$

EFPLAB1: Lab Experiment Venturi

Volume flow rate: l/s