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derive continuity equation

vishnu , 10 Years ago
Grade 11
anser 3 Answers
mohammad

Last Activity: 10 Years ago

p1a1v1=p2a2v2 or A1V1=A2V2

chaitnyakishore

Last Activity: 10 Years ago

Let us consider a tube AB of varing cross-section with water is flowing through that tube. At side A, area of cross-section be A1 velocity of fluid be v1 At side B, area of cross-section be A2 velocity of fluid be v2 and density of water be d and let A1>A2 Now v=distance travelled/time=l/t --->l=vt ---> Mass of fluid entered the tube at A in tseconds, m1=dV1=dAl=dA1v1t ----->(1) ---> Mass of fluid leaved the tube at B in tseconds, m2=dV2=dAl=dA2v2t ----->(2) But mass of fluid which entered into the tube is equal to the mass of fluid leaved the fluid. Therefore from equations (1) and (2) m1=m2 dA1v1t=dA2v2t Therefore A1v1t=A2v2t Therefore Av=constant

sivakrishna

Last Activity: 10 Years ago

Consider the mass of a fluid entering a at A in t seconds M1=density*A1*V1*t Mass of the fluid leaving the tube at B in t seconds M2=A2*density*V2*t We know that M1=M2, density*A1*V1*t=density*A2*V2*t A1*V1=A2*V2 Therefore A1*V1=constant

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