# Tag Info

## New answers tagged flow

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Continuity is just the principle of conservation of mass in differential form. The full continuity equation is (in index notation): $\frac{\partial \rho}{\partial t} = -\frac{\partial }{\partial x_i}(\rho u_i)$ For example, consider an infinitesimal control volume (CV). The equation says that the local $\rho$ (inside the CV) will decrease in time if the ...

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The book derives the equation of continuity, which states that the cross-sectional area times the velocity of a flow is always constant. But nowhere in the derivation does the textbook explicitly assumes that the flow is laminar. So, does the equation hold for turbulent flows too? That is only a special case of the equation of continuity for situation ...

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In order to have such a relation, your flow needs to be be stationary, which is never the case for turbulent flows. The conservation of the mass gives you the local continuity equation. $$\partial_t \rho+ \nabla . (\rho \vec{v})=0$$ For a stationary problem without sources, Ostrogradsky's theorem allows you to reach: $$\oint_S \vec{v}.d\vec{S}=0$$ But ...

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If this were a mechanical pump, then the work done per unit volume pumped would be: $$W = VP$$ where $V$ is the volume pumped and $P$ is the pressure increase across the pump. According to Wikipedia the volume pumped per heartbeat (at 72 bpm - does it change with pulse rate?) is about $70$ cubic centimetres per beat, which is $7 \times 10^{-5}$ m$^3$. ...

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For most plumbing applications, each obstruction has a $C_V$ value and the flow is $C_V \Delta p^2$, where $\Delta p$ is the pressure drop across the obstruction. As you need to flow more water through the hole, you need more pressure behind it, which means more depth of water in the bucket. In this approximation, as long as the bucket is tall enough, you ...

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Bernoulli's principle and conservation of mass can give you a simple approximation to an equilibrium solution to the problem: $$\frac{1}{2}v^2+gh+\frac{p}{\rho} = constant$$ and $$\dot{m}_{in} = \rho A_{hole} v_{hole}$$ Where $\dot{m}_{in}$ is the mass flux of fluid into the bucket. Assuming zero velocity at the fill point of the bucket and pressure at ...

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I agree with this result. First of all, the math is correct, though $$R = \frac{1000}{76 + \frac{20}{5/12}} \approx 8.06 \ m$$ but the change to your result is negligible. Second, it is consistent with the Manning Formula $$v = \frac{1}{n} R^{2/3} S^{1/2}$$ for your calculated velocity, slope, and ...

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