To determine the drag force in pounds, p is in units of pound-seconds 

 per foot 4 , the area in square feet, and the velocity in feet per second. 

 The coefficient of drag, Cp , is dimensionless and retains the same 

 value as in the kilogram-meter-second system. 



Tabulated values of drag coefficients are generally not available for 

 free-surface flow at high Reynolds numbers. Therefore, existing tables 

 of drag coefficients must be used to establish maximum coefficients to 

 ensure safe design. Table 6 gives examples of drag coefficients. 



Hallermeier (1976) discusses the importance of the parameter, u 2 /(gd), 

 where d is the projected horizontal dimension of the structure trans- 

 verse to the direction of flow. Where this parameter approaches unity 

 there are strong unidirectional free-surface flow effects. In that case, 

 the coefficients of drag, Cp, given in Table 6 may be too low. Individ- 

 ual model tests would be required to determine a more exact interaction 

 between the tsunami and the structure. 



For cases where flow does not overtop a structure, and where there 

 is no underflow, the flow may be treated as flow around an "infinitely 

 long" structure where the ground and the free surface define the bounda- 

 ries of a layer of fluid. For example, flow around a vertical cylindrical 

 storage tank would be treated as flow around an infinitely long cylrnder 

 in order to obtain a drag coefficient. 



In cases where there are overtopping and underflow, the ratio of 

 length-to-width for the structure should be determined. This ratio should 

 then be used for determining the coefficient of drag. 



For a situation in which there is either overflow or underflow^ the 

 coefficient of drag can be determined by using an approximation. Assume 

 that the depth of flow around the structure is twice the actual depth, 

 and that the height of the structure is equal to twice the wetted height. 

 Then obtain a coefficient of drag as if there were both underflow and 

 overflow (see Fig. 67). An example of this type of calculation follows: 



************** EXAMPLE PROBLEM 24 ************** 



GIVEN : A flat-sided structure is 14 meters wide and normal to the 

 direction of flow. The structure is 3.5 meters (11.5 feet) high and 

 supported on columns so there is a 1 .5-meter-high (4.9 feet) open space 

 under the base of the structure. The tsunami surge has a depth of 

 2.5 meters, giving a wetted height on the structure equal to 1.0 meter 

 (3.3 feet). 



FIND : 



(a) The coefficient of drag of the structure, and 



(b) the coefficient of drag of a similar structure located at ground 

 level with no underflow. 



179 



