<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-02-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000077360</issuerCik>
        <issuerName>PENTAIR plc</issuerName>
        <issuerTradingSymbol>PNR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001257864</rptOwnerCik>
            <rptOwnerName>GARDEN EDWARD P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>280 PARK AVENUE, 41ST FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10017</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Please see remarks below</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001345471</rptOwnerCik>
            <rptOwnerName>TRIAN FUND MANAGEMENT, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>280 PARK AVENUE, 41ST FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10017</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Please see remarks below</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2016-02-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>80041</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>47.2633</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>13761918</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Please see explanation below</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2016-02-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>49959</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>47.5076</value>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>13811877</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Please see explanation below</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2016-02-18</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>110473</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>47.8082</value>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>13922350</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Please see explanation below</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2016-02-18</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>87226</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>48.2291</value>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>14009576</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Please see explanation below</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2016-02-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>326312</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>47.9442</value>
                    <footnoteId id="F7"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>14335888</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Please see explanation below</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The price shown in Column 4 is a weighted average purchase price. The price range for the purchases is $46.46 to $47.46. The Reporting Persons undertake to provide upon request by the staff of the Securities and Exchange Commission, the Issuer or a security holder of the Issuer, full information regarding the number of shares purchased at each separate price.</footnote>
        <footnote id="F2">Trian Fund Management, L.P (&quot;Trian Management&quot;) serves as the management company for Trian Partners, L.P., Trian Partners Master Fund, L.P., Trian Partners Master Fund (ERISA), L.P., Trian Partners Parallel Fund I, L.P., Trian Partners Strategic Investment Fund II, L.P., Trian Partners Strategic Investment Fund-A, L.P., Trian Partners Strategic Investment Fund-N, L.P., Trian Partners Strategic Investment Fund-D, L.P., Trian Partners Fund (Sub)-G, L.P., Trian Partners Strategic Fund-G II, L.P., Trian Partners Strategic Fund-G III, L.P. and Trian Partners Strategic Fund-K, L.P. (collectively, the &quot;Trian Entities&quot;)</footnote>
        <footnote id="F3">(FN 2, contd.) and as such determines the investment and voting decisions of the Trian Entities with respect to the shares of the Issuer held by them. Mr. Garden is a member of Trian Fund Management GP, LLC, which is the general partner of Trian Management, and therefore is in a position to determine the investment and voting decisions made by Trian Management on behalf of the Trian Entities. Accordingly, Mr. Garden and Trian Management may be deemed to indirectly beneficially own (as that term is defined in Rule 13d-3 under the Securities Exchange Act of 1934) the shares beneficially owned by the Trian Entities. The Reporting Persons disclaim beneficial ownership of such shares except to the extent of their respective pecuniary interests therein and this report shall not be deemed an admission that the Reporting Persons are the beneficial owner of such securities for purposes of Section 16 or for any other purpose.</footnote>
        <footnote id="F4">The price shown in Column 4 is a weighted average purchase price. The price range for the purchases is $47.465 to $47.58. The Reporting Persons undertake to provide upon request by the staff of the Securities and Exchange Commission, the Issuer or a security holder of the Issuer, full information regarding the number of shares purchased at each separate price.</footnote>
        <footnote id="F5">The price shown in Column 4 is a weighted average purchase price. The price range for the purchases is $47.39 to $48.03. The Reporting Persons undertake to provide upon request by the staff of the Securities and Exchange Commission, the Issuer or a security holder of the Issuer, full information regarding the number of shares purchased at each separate price.</footnote>
        <footnote id="F6">The price shown in Column 4 is a weighted average purchase price. The price range for the purchases is $48.04 to $48.47. The Reporting Persons undertake to provide upon request by the staff of the Securities and Exchange Commission, the Issuer or a security holder of the Issuer, full information regarding the number of shares purchased at each separate price.</footnote>
        <footnote id="F7">The price shown in Column 4 is a weighted average purchase price. The price range for the purchases is $47.68 to $48.30. The Reporting Persons undertake to provide upon request by the staff of the Securities and Exchange Commission, the Issuer or a security holder of the Issuer, full information regarding the number of shares purchased at each separate price.</footnote>
    </footnotes>

    <remarks>Commencing on September 21, 2015, Mr. Garden has the right to attend, and participate in, all meetings of the Board of Directors of the Issuer in a nonvoting participant capacity, as further detailed in the letter agreement dated September 7, 2015 by and among the Issuer, Mr. Garden and the
other parties thereto that is included as Exhibit 2 to the Schedule 13D/A filed by Trian Fund Management, L.P. with the Securities and
Exchange Commission on September 8, 2015.</remarks>

    <ownerSignature>
        <signatureName>Daniel R. Marx, Attorney-In-Fact for Edward P. Garden</signatureName>
        <signatureDate>2016-02-19</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Daniel R. Marx, Attorney-In-Fact for Edward P. Garden, member of the general partner of Trian Fund Management, L.P.</signatureName>
        <signatureDate>2016-02-19</signatureDate>
    </ownerSignature>
</ownershipDocument>
