Dimensioning of an hydraulic system

for water bombing from an aircraft



Setting up

We choose to validate our program by comparing our results with those obtained thanks to an experiment set at IMFT (Toulouse Institute of Fluid Mechanics).

To be able to make comparisons between experimentation and real size tank in an aircraft, we have to identify similarity parameters and create dimensionless numbers. To that end, we used the Vaschy-Buckingham's theorem.

First, we identify the independent parameters which are necessary to describe the system:

Regarding geometry:

  • $H, l, L$, the dimensions of the tank
  • $l_s, L_s$ the dimensions of the exit

Regarding the fluid:

  • $\rho, \mu$ the density of water, the viscosity of water
  • $h_{water}$ the height of water in the tank

Regarding the environment:

  • $g$, the constant of gravity
  • $P$ the pressure

We obtain 11 parameters.

To simplify, we decide to consider that the tank is a cube. Besides, the trap door used for the experiment is circular and the tank in the lab has a free surface, the pressure at the top of the tank is the same than at the exit.


As a consequence, we can remove 3 parameters. The new system is:

Regarding geometry:

  • $l$ the dimension of the tank
  • $a$ the diameter of the exit

We have 6 parameters and 3 dimensions, we define:

  • the length by $a$
  • the mass by $\rho$
  • the time by $g$

We obtained 3 dimensionless numbers:



$Re=\rho \frac{a \sqrt{ga}}{\mu}$

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