R RuchiJay New member Joined Jun 12, 2011 Messages 1 Jun 12, 2011 #1 Please help me to integrate this eqn. with respect to r 1/r * d/dr(rh^3 dp/dr) = 6nu dh/dr + 12nv I need to find dp/dr
Please help me to integrate this eqn. with respect to r 1/r * d/dr(rh^3 dp/dr) = 6nu dh/dr + 12nv I need to find dp/dr
S soroban Elite Member Joined Jan 28, 2005 Messages 5,584 Jul 15, 2011 #2 Hello, RuchiJay! This is a strange problem. .Where did it come from? \(\displaystyle \text{Integrate with respect to }r.\) . . \(\displaystyle \frac{1}{r}\cdot \frac{d}{dr}\!\left(rh^3\frac{dp}{dr}\right) \:=\: 6nu\frac{dh}{dr} + 12nv\) \(\displaystyle \text{I need to find }\frac{dp}{dr}\) Click to expand... \(\displaystyle \text{I will assume that only }p\text{ and }r\text{ are variables.}\) \(\displaystyle \text{Multiply by }r\,dr\!:\;\;d\left(rh^3\frac{dp}{dr}\right) \;=\;6nur\,dh + 12nvr\,dr\) \(\displaystyle \text{Integrate: }\:\int\! d\left(rh^3\frac{dp}{dr}\right) \;=\;6nur\!\!\int\! dh + 12nv\!\! \int\! r\,dr\) . . . . . . . . . . . . . \(\displaystyle rh^3\frac{dp}{dr} \;=\;6nur\,h + 6nv\,r^2 + C\) . . . . . . . . . . . . . \(\displaystyle rh^3\frac{dp}{dr} \;=\;6nr(uh + vr) + C\) . . . . . . . . . . . . . . . \(\displaystyle \frac{dp}{dr} \;=\;\frac{6n(uh + vr) + C}{h^3}\)
Hello, RuchiJay! This is a strange problem. .Where did it come from? \(\displaystyle \text{Integrate with respect to }r.\) . . \(\displaystyle \frac{1}{r}\cdot \frac{d}{dr}\!\left(rh^3\frac{dp}{dr}\right) \:=\: 6nu\frac{dh}{dr} + 12nv\) \(\displaystyle \text{I need to find }\frac{dp}{dr}\) Click to expand... \(\displaystyle \text{I will assume that only }p\text{ and }r\text{ are variables.}\) \(\displaystyle \text{Multiply by }r\,dr\!:\;\;d\left(rh^3\frac{dp}{dr}\right) \;=\;6nur\,dh + 12nvr\,dr\) \(\displaystyle \text{Integrate: }\:\int\! d\left(rh^3\frac{dp}{dr}\right) \;=\;6nur\!\!\int\! dh + 12nv\!\! \int\! r\,dr\) . . . . . . . . . . . . . \(\displaystyle rh^3\frac{dp}{dr} \;=\;6nur\,h + 6nv\,r^2 + C\) . . . . . . . . . . . . . \(\displaystyle rh^3\frac{dp}{dr} \;=\;6nr(uh + vr) + C\) . . . . . . . . . . . . . . . \(\displaystyle \frac{dp}{dr} \;=\;\frac{6n(uh + vr) + C}{h^3}\)
