如图1-31所示。一高位槽通过一总管及两支管A、B分别向水槽C、D供水。假设总管和支管上的阀门[tex=1.214x1.214]LMGHnJOuoAlOtfpD7uFSHg==[/tex]、[tex=1.429x1.214]df78nhB80QixGczUoPkDgA==[/tex]、[tex=1.429x1.214]iZKzOdlsTH56krdWNtOW1A==[/tex]均处在全开状态，三个水槽液面保持恒定。试分析，当将阀门[tex=1.429x1.214]+H5sF/kuLgxoyAnLBAvfLQ==[/tex]关小，总管和各支管的的流量及分支点前0处的压力如何变化。各管段的λ均可视为常数。[img=422x300]179a8ac4d50c604.png[/img]

2022-06-30

如图1-31所示。一高位槽通过一总管及两支管A、B分别向水槽C、D供水。假设总管和支管上的阀门[tex=1.214x1.214]LMGHnJOuoAlOtfpD7uFSHg==[/tex]、[tex=1.429x1.214]df78nhB80QixGczUoPkDgA==[/tex]、[tex=1.429x1.214]iZKzOdlsTH56krdWNtOW1A==[/tex]均处在全开状态，三个水槽液面保持恒定。试分析，当将阀门[tex=1.429x1.214]+H5sF/kuLgxoyAnLBAvfLQ==[/tex]关小，总管和各支管的的流量及分支点前0处的压力如何变化。各管段的λ均可视为常数。[img=422x300]179a8ac4d50c604.png[/img]

答案：

解 （1）总管和各支管流量变化分析分别在液面1-1'与2-2'和液面1-1'与3-3'间列柏努利方程，取单位质量流体为基准：[tex=26.0x2.714]AhqTQuOWUX0yOZ0jqR6bIBNmh9QLHtGt6QbC2dAhlSO8NJw7I7peaMvuYgT5SQyb5y6Pe8e3kBmAI+nmWZ26LPyJVbb9RVurrvtreAioPJngBr7rTJtxyiv7x4sexQWXwR3n6jSr0ck05vAIvDxniXI4Bka+nQ3+JDKAbcaee3uUJZ6zXRP7eB5+SZ34/E05t9XSNMucTyBBMGKdE+pPdUnzKIVxKD5aGANqyqk4xS9BxnuMh06pkUfuqYb3lcRNEWmIJXwucFfdaE3TQcqGhw==[/tex][tex=17.929x2.714]fHcPcU094vDNB9TTEfg8GiYxoBZ5sIFZ1Kfss5ze2h6IQjf7k3GOifdc+jYtrGuPT3Q4WZojAbo2GrhJ3O6GvDrrqpTwyyt1V9CrtRbipIGysuTPKLWJTaM7R5n/iH9ynCeuxRsibDT0b2c3cCXIMOmP7jZALuzlbEyL+JDtsoiLjwUJRQZAP/LF4tR74EoMSqBPhCUbAVqK25YjRr1MH6ezWkVxPJBwT5EQUUMeG7M=[/tex]（A）[tex=26.214x2.714]HhKE4JJv7yP9dFpMMsilOzeN+Zw6NipgI7U7sdgDK3lPXaL3J2seFxmJLVbpqk0Zzbe6ac50UIiYmzMt2D5Zv1VApH7yWKXGVT9+BlkQKMvc9fAbkvKYZa9qIsJ/NQpPqPaso34wwh6pBQQ7UlhjygWMzoJfmYV40IlpxVzaDL+pA4TOPXuDqN+4jnkUVcAn3cHZ/kf35XeQpWfzVPXhk+utajyNr3kYLPLlKcHKlWSn32ZpOU7zXVo/USEKfQmrwj/syXryZ0Wf5PQbdgb2uw==[/tex][tex=18.0x2.714]fHcPcU094vDNB9TTEfg8GiYxoBZ5sIFZ1Kfss5ze2h6IQjf7k3GOifdc+jYtrGuPT3Q4WZojAbo2GrhJ3O6GvDrrqpTwyyt1V9CrtRbipIGysuTPKLWJTaM7R5n/iH9y6HpjoymH5wS6mHIaRVXqiV5uDs75pZ13sJU2Y8tyZ2WMoQw+M+qpDhGdmXQTtCe035pMVD1PbLh3OH4qC0g7wYpAGS9EhJdU7iybomhOldE=[/tex]（2）令：[tex=28.214x2.714]SQHr0F13BI0KC1biXFpns5Cz0XSDR+tiT2y/L8Z8V9ynI3kIcF2f94TWcpQKTSasf/bqSzCaRmK9Dyre2Ufcg2wGycMRFkG8ZgPTcsGAQJV+cEjiOMommJh/2wX6JbAxZv6g0dPIJoiLD0626iKK8xWEcV03Dzie2PohqcScZBNGhO2RUdRQz2j/qMFApUdNq3nwwWa/huGlnYNsUn30Z/9S/HDnzD1axa1WcES9hdBr4ZabM29qmR65DHjeb2I2W13/RFqjfk/1QFHdKPK80bPGlkjPTQdg1u6st8DaGlR4r8gYCKhQrcc1xlU2hN+o[/tex][tex=1.143x1.214]F09X0tilrMkXjlrZyUwtzw==[/tex]、[tex=1.286x1.214]XDDZ8+bnQ36EIbFh0YRICw==[/tex]、[tex=1.357x1.214]P6Iiq4HL2vkQ0Y6T8DF0cA==[/tex]分别代表各管段的阻力特性，代人式(1)、式(2)中:[tex=9.5x1.5]VDUEiHFMCcNzN1vCMSPsmBFWKgzQBoepcVyNzTeQwTqAodGrSSCtyB0ZX1GbRMn+Q8+33z0hwjcSdt7ixVcKzQ==[/tex]（3）[tex=9.357x1.5]lHg5llQu/ARDR6hxd3nbtaLorQtQmHDXhPG1jW2AQTnAQutDAokl+SFucAaFeTgtGcNcTbrIR3LoWzgJ9L9WPw==[/tex]（4）再由分支点处的质量恒算得:[tex=4.714x1.214]ZhlkXMEImvOqXnqcwbpmQCBp6SwjX+k52g4ttGb0ppc=[/tex]（5）联立式(3)、式(4)、式(5)可得: [tex=17.714x3.429]Wwd78bDjQU3VIKfhTdHyn4+Ikre9omoHHM/CWVZquz7Fgssy4rIffKh84XrmDbofCviaSTRFteZMcXUu4xEfiHJiBsJyNSkRnA2Sc7qzE4kAAVXRcnlqFtaic+rXbkVCAE9epKFFm8Mlt/0UhRChrA==[/tex]（6）由上式分析，当阀门[tex=1.429x1.214]+H5sF/kuLgxoyAnLBAvfLQ==[/tex]关小时，式中的[tex=7.643x1.214]6STkv1MBDlzlQ0Gvsz7Vbl+B66JjDpOByIGyw68ZnIMbYKczvK5yv9buvNSfOpsW[/tex]均不变，而[tex=1.929x1.214]QrbN14nmtR+pUSmx/w5KJXKwrOGlOnpIIn/pTxmR3lA=[/tex]增大，即[tex=1.286x1.214]XDDZ8+bnQ36EIbFh0YRICw==[/tex]增大。若假设[tex=0.929x1.214]yMRdxmM1/45eZMNiHw07Zw==[/tex]不变或增大，可推出式(6)两边不等，故只能[tex=0.929x1.214]yMRdxmM1/45eZMNiHw07Zw==[/tex]减小。这种方法称为排除法。（2）0处压力[tex=1.0x1.214]994QmpsT6Dh5U6wp25rC2A==[/tex]变化分析在截面1 - 1'和0点所在截面间列柏努利方程:[tex=10.929x2.786]NILTCizqr0Sx+7/4ZIizeYDCr5Y+S9VdS7c+s4zrMCHRA9epV/XbQl6eX05/ywh2HpylhGVgszzcSMYS6EihauWcu8uPrx2dF4bYXAdSeLk=[/tex]当阀门[tex=1.429x1.214]+H5sF/kuLgxoyAnLBAvfLQ==[/tex]关小时，上式中[tex=4.286x1.214]alZwnalJ76T1XQFoHpgtSJpBidmtMQK2apVK0uwTDoA=[/tex]均不变，而[tex=0.929x1.214]yMRdxmM1/45eZMNiHw07Zw==[/tex]减小即[tex=1.143x1.0]2/sNVUC87nq7QxiMDm/uJg==[/tex]减小，故[tex=1.0x1.214]994QmpsT6Dh5U6wp25rC2A==[/tex]增大。

举一反三

内容

0
设方程[tex=5.643x1.357]r1/libd7OSlfzu89S23PgtZT9idtAY89YiA87iP4eQ4=[/tex](1) 当常数 [tex=1.429x1.214]rkgrF+YaaESwSQDjR6KfWg==[/tex] 满足何种关系时,方程有唯一实根?(2) 当常数 [tex=1.429x1.214]rkgrF+YaaESwSQDjR6KfWg==[/tex] 满足何种关系时,方程无实根.
1
如[例22]图所示水塔经输水钢管向B、C、D处供水，已知[tex=6.5x1.5]9SqkRYzQZTXJKwntawA4cfVrcoaeNvLgI2oDrSU+7aHTHpsH+MA22nfRpq2FiwW9[/tex],[tex=6.5x1.5]qfm447c3WMJbPvQusCxKGicJ8aQh1lbBUaiEFHpIEclDxO3YSzjToVGTkgzMCWvZ[/tex],[tex=6.857x1.5]Jsaqa41CgP4j/pdpWIB+Q3fsHDflNM5IympLULbr+NXr2iESO49I2jlilDOn1fA6[/tex], 管长[tex=3.786x1.214]4lyXqOHwiwQHhFd9RYx2g/cssDT52sxVy6fqUCJcdME=[/tex]，[tex=4.786x1.214]ns4er6IE/vkCNQ4T78umW0EqAVglD1mptkWAS7YgNF8=[/tex]，[tex=4.786x1.214]GZzg6AabRoZkpxDj2p8FPN+TfI0nO8bxcV6HVAu4xPE=[/tex]，要求D点保持10m的自由水头，各管段的水力坡度J相同，各管段的粗糙系数[tex=4.214x1.0]nu75x091TiBAbtH6aZWSfQ==[/tex]，水塔水面高程为30m，试求各管段的管径。[img=359x235]17da945dcdee8d0.png[/img]
2
在图中, 已知 [tex=3.786x1.214]DOjAjCZzjF43+3AQXLLn6g==[/tex], 求 [tex=3.786x1.286]SgGSC7KcBedOVsmzEidykyw+grWDrxwxtL/KbeFZ4W0=[/tex]及[tex=1.429x1.214]c2LrKowfYMU8Zao/aqpnlg==[/tex] 。[img=514x236]17e3a0f5f7fe5ff.png[/img]
3
试求图 5-29 所示等截面圆弧曲杆[tex=0.786x1.0]XUo+oVq0EXNG7rY4rJKp8w==[/tex]点的坚向位移[tex=1.429x1.0]a3mBK50EUc4P09k1hLsQqpiVRdNLTICIRti3FERSDZE=[/tex] 和水平位移[tex=1.429x1.214]D9WbpzJJzgEQ7yfNiucHVzsIgKWblUalGXMhwAqm9HQ=[/tex]。设圆弧 [tex=1.5x1.0]osX852S+wV8CwpEm4xtoUQ==[/tex] 为 [tex=0.786x2.357]skQrMgG+4NxSwrl/6DdfjQ==[/tex]个圆周, 半径为[tex=2.286x1.214]XQG+skBaTp6rojgvx4xt+y6Q0a3h040NEmTsVndVDdg=[/tex]为常数。[img=196x274]17cf4ab5c670417.png[/img]
4
有一并联管路, 输送[tex=2.143x1.071]mrYnzy2TFRKIW+QJLIWRIw==[/tex] 的水。若总管中水的流量为 [tex=4.357x1.5]5URolbkikD2jOKwTX/Sv4upc/vSKAnRKyEZ5jbbCoww=[/tex], 两根并联管的管径与管长分别为 [tex=18.786x1.214]mUfS4mIb7+ksx29B38MXVV6GjPwwoHEPRQgCotDrG9li8/x1Xpt956uUTly79awPVwi49fteIYz/Po3VmOP12A==[/tex] 。试求两根并联管中的流量各为若干? 管壁绝对相糙度为 [tex=3.071x1.0]SWaWXMfH1FAhQESq0bhhIQ==[/tex] 。