We know pleural effusion (hydrothorax) is disproportionately more common on right side in cardiac failure.Though its a well observed phenomenon, the mechanism of which has not been clear to us. It could be due to multiple anatomical , physiological factors.

*The are right and left lymphatic (Thoracic) ducts that drain the corresponding lungs and pleural space . There can be overlap and contribute to the differential occurrence of pleural effusion
Reference
A meticulous paper written some 75 years ago (1946) from Harvard medical school teach us some important points in this phenomenon.
There is still lot, to be understood about pleural effusion in cardiac failure. We need to know why some pleural effusions tend to occur independent of hydrostatic forces. It is also noted long-standing transudative effusions can become true exudates. Role of local pleural capillary hypoxia resulting increasing permeability is underestimated.Hepatic congestion and trans-abdominal seepage of fluid is a distinct possibility.
One more area we are not clear is the relationship between the genesis of pericardial effusion in cardiac failure and concomitant pleural effusion. Post operatively , after univentricular repair (as in Fontan ), pleural effusions can be much problematic with high venous pressure interfering with pleural drainage.
Impact on symptoms
Finally, even mild pleural effusion can increase the work of breathing and result in dyspnea which is out of proportion to cardiac dysfunction.While we expect the diurteics to clear the effusion of cardiac failure, it doesn’t happen always arguing for a non transudative mechanism in at least some of them.
Further reading
Discerned readers are advised to study the pleural space dynamics in detail.
Link to the original Article of Edgar Mcpeak and Levine 1946