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Stock-Based Compensation Plans (Information Regarding Restricted Shares) (Details) (USD $)
In Millions, except Share data, unless otherwise specified
12 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Restricted Stock      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Unearned compensation costs $ 30.6us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
$ 31.5us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
 
Recognition of unearned compensation, (years) 1 year    
Fair value of Restricted Shares vested 34.8us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
34.9us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
36.4us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
Stock-based compensation expense 42.7us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
35.8us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
35.4us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
Related income tax benefit (14.6)us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
(12.3)us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
(12.0)us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
Net stock-based compensation expense $ 28.1us-gaap_AllocatedShareBasedCompensationExpenseNetOfTax
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
$ 23.5us-gaap_AllocatedShareBasedCompensationExpenseNetOfTax
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
$ 23.4us-gaap_AllocatedShareBasedCompensationExpenseNetOfTax
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
Shares      
Outstanding — beginning of year 2,020,678us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Granted 734,187us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Canceled (788,468)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Canceled (109,849)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Outstanding — ending of year 1,856,548us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
2,020,678us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
 
Weighted Average Grant-Date Fair Value      
Outstanding — beginning of year $ 44.68us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Granted $ 64.35us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Vested $ 44.10us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Canceled $ 51.63us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
   
Outstanding — ending of year $ 52.29us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
$ 44.68us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockMember
 
Restricted Stock | Maximum      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
General expiration period, from date of grant or time of termination 3 years    
General vesting period 3 years    
Restricted Stock | Minimum      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
General expiration period, from date of grant or time of termination 1 year    
General vesting period 1 year    
Performance Shares      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
General vesting period 36 months    
Period for achieving performance targets on performance based units (years) 3 years    
Minimum range of vesting provisions 0fls_ShareBasedCompensationArrangementsByPerformanceBasedUnitsMinimumRangeOfVestingProvisions
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
   
Maximum range of vesting provisions 1,580,000fls_ShareBasedCompensationArrangementsByPerformanceBasedUnitsMaximumRangeOfVestingProvisions
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
   
Estimated vesting of shares based on performance shares 1,244,000fls_ShareBasedCompensationArrangementByShareBasedPaymentAwardPerformanceBasedUnitsExpectedToVestOutstandingNumber
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
   
Shares      
Outstanding — ending of year 811,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
   
Performance Shares | Maximum      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting percentage of grants, depending on achievement of specific performance targets 200.00%fls_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPercentage
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
/ us-gaap_RangeAxis
= us-gaap_MaximumMember
   
Performance Shares | Minimum      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting percentage of grants, depending on achievement of specific performance targets 0.00%fls_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPercentage
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
/ us-gaap_RangeAxis
= us-gaap_MinimumMember