Question
Fri March 06, 2015 By: Sanmit Ratnaparkhi

Dear sir,
Can u please help me to solve question
Water is flowing through a cylindrical pipe of internal diameter 2 cm into a cylindrical tank of base radius 40cm at the rate of 0.4m/s.determine the rise in level of water in the tank in half an hour.
And also iam not able to understand upstream and downstream questions pls help with an example
 

Expert Reply
Prasenjit Paul
Sat March 07, 2015
L e t space t h e space r i s e space i n space t h e space l e v e l space o f space w a t e r space i n space t h e space tan k space b e space apostrophe h apostrophe. V o l u m e space o f space w a t e r space i n space t h e space tan k space equals straight pi cross times left parenthesis 40 right parenthesis squared cross times straight h Volume space of space water space flowing space per space second space from space the space pipe equals straight pi cross times left parenthesis 2 right parenthesis squared cross times 0.4 cross times 100 Volume space of space water space flowing space from space the space pipe space in space 30 space minutes equals straight V straight o straight l straight u straight m straight e space straight o straight f space straight w straight a straight t straight e straight r space straight i straight n space straight t straight h straight e space tan straight k rightwards double arrow straight pi cross times left parenthesis 2 right parenthesis squared cross times 0.4 cross times 100 cross times 30 cross times 60 equals straight pi cross times left parenthesis 40 right parenthesis squared cross times straight h rightwards double arrow straight h equals fraction numerator straight pi cross times left parenthesis 2 right parenthesis squared cross times 0.4 cross times 100 cross times 30 cross times 60 over denominator straight pi cross times left parenthesis 40 right parenthesis squared end fraction rightwards double arrow straight h equals 180 space cm therefore rise space in space the space level space of space water space in space the space tank space equals 180 space cm  Boats space and space Stream space problem colon let space the space speed space of space the space boat space in space still space water space be space apostrophe straight b apostrophe space and space the space speed space of space the space stream space be space apostrophe straight s apostrophe  In space case space of space straight a space boat space moving space upstream comma space boat space is space moving space against space the space stream comma Speed space of space boat space in space Upstream equals straight b minus straight s space left square bracket Since space speed space of space stream space will space be space opposite space to space that space of space the space boat right square bracket  In space case space of space straight a space boat space moving space downstream comma space boat space is space moving space with space the space stream comma Speed space of space boat space in space downstream equals straight b plus straight s space left square bracket Since space speed space of space stream space will space be space same space as space that space of space the space boat right square bracket  Example colon straight A space boat space takes space 1 space hour space to space cover space straight a space distance space of space 4 space km space with space the space stream space and space takes space 5 space hours space to space return space the space same space distance. Find space the space speeds space of space the space boat space and space the space stream.  Solution colon space let space the space speed space of space the space boat space in space still space water space be space apostrophe straight b apostrophe space and space the space speed space of space the space stream space be space apostrophe straight s apostrophe Speed space of space boat space in space Upstream equals straight b minus straight s Speed space of space boat space in space downstream equals straight b plus straight s 1 equals fraction numerator 4 over denominator straight b plus straight s end fraction straight b plus straight s equals 4....... left parenthesis straight i right parenthesis 5 equals fraction numerator 4 over denominator straight b minus straight s end fraction straight b minus straight s equals 1........ left parenthesis ii right parenthesis Adding space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma 2 straight b equals 6 straight b equals 3 space km divided by hr straight s equals 1 space km divided by hr Speed space of space boat space in space still space water space equals space 3 space km divided by hr Speed space of space stream space equals space 1 space km divided by hr
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