# Calculating Reynolds number in a water tunnel

I am trying to calculate the Reynolds number of a flow that I will be creating in a water tunnel. Reynolds number ($$RE$$) is given by the following where $$\rho$$ gives fluid density, $$u$$ gives velocity of the fluid, $$L$$ gives the characteristic linear dimension, and $$\mu$$ is the dynamic viscosity of the fluid. $$RE=\frac{{\rho}{u}{L}}{\mu}$$

In my system, the flow velocity is $$0.5$$ m/s. The density of water is $$997$$ kg/m$$^{3}$$ and the value I am using for the dynamic viscosity of water is $$8.9 \times 10^{-4}$$ Pa/s. The viewing area of the tunnel that my object will be in is a rectangle with a square cross sectional area of $$0.0225$$ m$${^2}$$. Plugging these values into the Reynold's number equation, however, gives me a value of $$\approx 84017$$.

Based on this paper, I am skeptical that I used an incorrect value. The paper reports a more powerful water tunnel with a significantly lower Reynolds number, $$15000$$.

Commercial water tunnels typically generate a momentum thickness based Reynolds number (Reθ) ∼1000, which is slightly above the laminar to turbulent transition. The current work compiles the literature on the design of high-Reynolds number facilities and uses it to design a high-Reynolds number recirculating water tunnel that spans the range between commercial water tunnels and the largest in the world. The final design has a 1.1 m long test-section with a 152 mm square cross section that can reach speed of 10 m/s, which corresponds to Reθ=15,000. Flow conditioning via a tandem configuration of honeycombs and settling-chambers combined with an 8.5:1 area contraction resulted in an average test-section inlet turbulence level <0.3% and negligible mean shear in the test-section core. The developing boundary layer on the test-section walls conform to a canonical zero-pressure-gradient (ZPG) flat-plate turbulent boundary layer (TBL) with the outer variable scaled profile matching a 1/7th power-law fit, inner variable scaled velocity profiles matching the log-law and a shape factor of 1.3.

I suspect that I may have used an incorrect value for $$L$$. Could anyone advise me where I went wrong? I do believe that the flow around my object, a turbine, is turbulent, however, I don't believe it is so much so as to having a Reynolds number of $$80000$$.

• There is no unique Reynolds number. If you want to compare with the paper you have linked to then you should use the same definition for length and velocity scales as they have done. – Deep Feb 28 at 5:03