def calculate_speed(**kwargs):
= (melting_temperature + background_temperature) / 2
mean_temperature = heat_capacity_ice * (melting_temperature - background_temperature) + latent_heat_melting_water
hm_star = np.pi * (0.5 * diameter) ** 2
area
= mass * gravity
force -= area * density_water * (length * gravity)
force
= density_ice / density_water
density_ratio
# thermal diffusivity:
= thermal_conductivity_water / (density_water * heat_capacity_water)
a_l
###################
### SOLUTION a) ###
###################
= 0.0 # YOUR SOLUTION HERE
speed
#######################
### SOULUTON a) END ###
#######################
return speed*(60.*60.) # m/h
Homework Template
- Your homework solution has to be handed in as a group solution via Moodle.
- Clearly state name and matriculation number of each student
0.1 Task A: import a full problem
Consider a stationary cylindrical glass with inner radius \(R\) and partially filled with water upto height \(H\). The ambient pressure is given by \(p_a\). The glass is now spun about its central axis with an angular velocity \(\Omega\), which causes the top surface of the water to form a parabolloid. A selected cross section of the stationary and spinning glass with fluid is shown in the figure.
Tasks
Task 1
In a rotating reference frame with angular velocity \(\Omega\), state the Bernoulli equation. What are the assumptions used to derive the equation?
Task 2
For the fluid spinning at \(\Omega\), calculate the difference in height of the fluid at points 1 and 2.
Task 3
Calculate the angular velocity of spinning \(\Omega_0\), at which the height of the fluid at point 1 is zero.
Task 4
For the fluid spinning at \(\Omega_0\), calculate the pressure at point 3 in terms of the of the ambient pressure \(p_a\)