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Revenue Recognition (Narrative) (Details) - USD ($)
 12 Months Ended
Aug. 31, 2021
Aug. 31, 2020
Aug. 31, 2019
Disaggregation of Revenue [Line Items]      
Accrued liabilities $ 25,658,000 $ 21,660,000  
Reduction to revenue 488,109,000 408,498,000 $ 423,350,000
Refund liability 500,000    
Contract assets 0 0  
Cash Discounts [Member]      
Disaggregation of Revenue [Line Items]      
Reduction to revenue 4,900,000 4,400,000  
Accounting Standards Update 2014-09 [Member]      
Disaggregation of Revenue [Line Items]      
Contract liabilities 3,700,000 1,400,000  
Contract liabilities recognized to revenue   1,400,000  
Accounting Standards Update 2014-09 [Member] | Rebate/Other Discounts [Member]      
Disaggregation of Revenue [Line Items]      
Accrued liabilities 8,400,000 7,500,000  
Reduction to revenue 28,700,000 20,700,000  
Accounting Standards Update 2014-09 [Member] | Cash Discounts [Member]      
Disaggregation of Revenue [Line Items]      
Allowance for cash discount $ 500,000 $ 500,000