1

The dynamics in the ocean can be described by the equation of motion $\frac{Du}{Dt}=-{\nabla}{\Phi}- \frac{1}{p}{\nabla}p- f\cdot u$ . Consider the motion of water in a full kitchen sink, with the water slowly draining out the bottom. The height of the water surface is estimated to vary by about 1 cm over horizontal distances of order 10 cm and typical water speeds in the sink are estimated to be 0.1 m/s. (i) Using the relevant equation(s), estimate the corresponding horizontal pressure gradients.

For a question like this are we imagining two point on the surface of a draining sink, seperated by

10cm and varying in height of 1cm, The inclusion of the water speed is confusing me can it just be ignored as the two points would be moving at the same speed?

Massin
  • 314
  • 1
  • 3
  • 20
  • Please review [this] on MathJax. You have some text that should clearly be $\LaTeX$, but it doesn't render properly. – Ross Millikan Mar 23 '15 at 05:18
  • I did what I could for the formatting. I don't know if $F$ and $f$ are the same, nor what font you wanted $F$ in. Please review and fix or comment. – Ross Millikan Mar 23 '15 at 05:26
  • Have corrected this – Massin Mar 23 '15 at 05:31
  • @RossMillikan I too am interested in solving this question. Are we to use the equation $$\text{pressure}=\frac{\text{force}}{\text{area}}?$$ – M B Feb 27 '20 at 04:47
  • 1
    For the static head you can just use $p=\rho g h$, the density of water times the height and the acceleration of gravity. I believe the dynamic pressure is $\frac 12 \rho v^2$, but it was long ago. – Ross Millikan Feb 27 '20 at 05:29

1 Answers1

0

Hint: how much pressure difference is there for 1 cm in water height? If that is the variation over 10 cm, the gradient is that difference divided by 10 cm.

Ross Millikan
  • 374,822
  • is it -gtan($\theta$) – Massin Mar 23 '15 at 05:26
  • where g is the gravitational constant and $\theta$ the angle between the two points – Massin Mar 23 '15 at 05:27
  • You need something about the density of water, no? I believe you can ignore the water velocity, but are supposed to justify that. How much pressure difference does that much velocity make? I believe it is small compared to the 1 cm of level difference. That is your justification. – Ross Millikan Mar 23 '15 at 13:48