Prototype-to-model scale ratios for horizontal lengths, vertical lengths, flow

velocity, and total discharge are given in Table 4.

**Table 4**

**Distorted Model Froude Scales**

**Scale**

**Ratio**

**Notation**

**Relationship**

*Xp / Xm*

*NX*

Horizontal length

*Zp / Zm*

*NZ*

Vertical length

*NX / NZ*

Ω

Model distortion

*NV = NZ*1*/*2

*Vp / Vm*

*NV*

Velocity

*NQ = NX:NZ*3*/*2 *= *Ω*:NZ*5*/*2

*Qp / Qm*

*NQ*

Discharge

Model scale was manipulated by specifying appropriate horizontal and

vertical length scales and the discharge scale. Two of the scales can be selected,

and the third is then constrained by the scale equations. For most test series it

was more convenient to keep the flow discharge constant for all experiments and

change the horizontal and vertical dimensions to suit the different model

distortions. This way the flow valve remained at the same setting and difficulties

in adjusting the flow rate to a precise value were avoided.

Solving the discharge scale equation for *N*Z gives:

2/5

*N*Q

*NZ *=

(33)

Ω

For a given distortion, Ω, and a specified discharge scale (usually *N*Q = 1), the

vertical length scale is determined, and the horizontal length scale is found as:

*N X *= Ω *N*Z

(34)

Once the scale ratios were determined, horizontal and vertical dimensions in the

distorted model could be determined based on the prototype target dimensions.

For constant discharge, water depths increased with distortion while the gap

distance decreased.

**Velocity measurements**

For each test series a velocity measurement grid was established. The grid

encompassed the primary region of interest and included points within the

turbulent and nonturbulent portions of the flow regime. The uniform, rectangular

grid positions were entered into the computer program, which controlled the

traversing system and acquired the data. Grid dimensions established for the

target condition were scaled appropriately for each distorted test so the

39

Chapter 5 Turbulence Scale Effects Experiments