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Revenue (Narrative) (Details) - USD ($)
 12 Months Ended
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Disaggregation of Revenue [Line Items]      
Total net sales $ 537,255,000 $ 518,820,000 $ 488,109,000
Accrued liabilities 30,000,000 27,161,000  
Contract liabilities 4,600,000 5,000,000  
Contract liabilities recognized to revenue   5,000,000  
Contract assets 0 0  
Rebate/Other Discounts      
Disaggregation of Revenue [Line Items]      
Total net sales 33,300,000 32,800,000  
Accrued liabilities 11,100,000 8,700,000  
Cash Discounts      
Disaggregation of Revenue [Line Items]      
Total net sales 5,600,000 5,200,000  
Allowance for cash discount $ 600,000 $ 500,000