Assignment/Reading 4, Physics 426 Fluid Mechanics
Reading (Participation only, very short answer)
- Ch 7, sections 11 to 13 non-linear steepening waves, hydrualic jumps, solitons.
R1: Why do waves tend to steepen?
Waves tend to steepen: why?
R2: Jump condition
What two quantities are conserved across a hydraulic jump?
R3: Solitary waves:
What two wave tendencies are balanced in a soliton?
Assignment
- Kiniematics
- Conservation of mass
A1: Streamlines in a corner flow (/10)
The flow in a 90-degree bend at the origin can be described by
\[u = y\]
\[v = x\]
- Derive and sketch the streamlines $\psi$ of the flow, where $u = \partial \psi / \partial y$ and $v = -\partial \psi / \partial x$:
- Contour the streamfunction on a computer
- where in the flow would you put the walls to make this a flow in a corner?
- Demonstrate analytically that the the flow is non-divergent.
- Demonstrate that it is close to non-divergent in your computer code.
A2: Multiple density mixing vat (/5)
Suppose we have a mixing vat, with one inflow at $q_1 = 2\ m^3\,s^{-1}$ and a fluid of density $\rho_1 = 1000\ kg\,m^{-3}$, and a second inflow with density $\rho_2 = 1030\ kg\,m^{-3}$, and an outflow with density $\rho_3 = 1028\ kg\,m^{-3}$. What must the outflow rate be if the fluids are incompressible?
Last Modified: 28 April 2024 Licence: Creative Commons Attribution required, non-commercial uses (CC BY-NC 4.0)