<!-- #region -->


 - Place the apparatus on the hydraulics bench, and ensure that the outflow tube is positioned above the volumetric tank to facilitate timed volume collections.
 - Level the apparatus base by adjusting its feet. (A sprit level is attached to the base for this purpose.) For accurate height measurement from the manometers, the apparatus must be horizontal.
 - Install the test section with the **14° tapered section** converging in the flow direction. If the test section needs to be reversed, the total head probe must be retracted before releasing the mounting couplings.
 - Connect the apparatus inlet to the bench flow supply, close the bench valve and the apparatus flow control valve, and start the pump. Gradually open the bench valve to fill the test section with water.
 - The following steps should be taken to purge air from the pressure tapping points and manometers:
    - Close both the bench valve and the apparatus flow control valve.
    - Remove the cap from the air valve, connect a small tube from the air valve to the volumetric tank, and open the air bleed screw.
    - Open the bench valve and allow flow through the manometers to purge all air from them, then tighten the air bleed screw and partly open the bench valve and the apparatus flow control valve.
    - Open the air bleed screw slightly to allow air to enter the top of the manometers (you may need to adjust both valves to achieve this), and re-tighten the screw when the manometer levels reach a convenient height. The maximum flow will be determined by having a maximum (h1) and minimum (h5) manometer readings on the baseboard.

If needed, the manometer levels can be adjusted by using an air pump to pressurize them. This can be accomplished by attaching the hand pump tube to the air bleed valve, opening the screw, and pumping air into the manometers.  Close the screw, after pumping, to retain the pressure in the system.

 - Take readings of manometers $h_1$ to $h_6$ when the water level in the manometers is steady. The total pressure probe should be retracted from the test section during this reading.
 - Measure the total head by traversing the total pressure probe along the test section from $h_1$ to $h_6$.
 - Measure the flow rate by a timed volume collection. To do that, close the ball valve and use a stopwatch to measure the time it takes to accumulate a known volume of fluid in the tank, which is read from the sight glass. You should collect fluid for at least **one minute** to minimize timing errors. You may repeat the flow measurement twice to check for repeatability. Be sure that the total pressure probe is retracted from the test section during this measurement.
 - Reduce the flow rate to give the head difference of about 50 mm between manometers 1 and 5 ($h_1-h_5$). This is the minimum flow experiment. Measure the pressure head, total head, and flow.
 - Repeat the process for one more flow rate, with the ($h_1-h_5$) difference approximately halfway between those obtained for the minimum and maximum flows. This is the average flow experiment.
 - Reverse the test section (with the **21° tapered section** converging in the flow direction) in order to observe the effects of a more rapidly converging section. Ensure that the total pressure probe is fully withdrawn from the test section, but not pulled out of its guide in the downstream coupling. Unscrew the two couplings, remove the test section and reverse it, then re-assemble it by tightening the couplings.
 - Perform three sets of flow, and conduct pressure and flow measurements as above.
<!-- #endregion -->

# 9. RESULTS AND CALCULATIONS

## 9.1. RESULTS

Enter the test results into the Raw Data Tables.

### Position 1: Tapering 14° to 21°


```python jupyter={"source_hidden": true}
from ipydatagrid import DataGrid
import pandas as pd


rd_1_1 = pd.DataFrame({"Test Section": r"h_1 h_2 h_3 h_4 h_5 h_6".split(), \
                                  "Pressure Head (mm)": [0.,0.,0.,0.,0.,0.], \
                                  "Total Head (mm)": [0.,0.,0.,0.,0.,0.], \
                                  "Volume (Liter)": [0., "-", "-", "-", "-", "-"], \
                                  "Time (sec)": [0., "-", "-", "-", "-", "-"]})
raw_data_1_1 = DataGrid(rd_1_1, \
                   editable = True, \
                   layout={"height": "180px"})
raw_data_1_1.auto_fit_columns = True

print("Test #1")
raw_data_1_1

```python jupyter={"source_hidden": true}
rd_1_3 = pd.DataFrame({"Test Section": r"h_1 h_2 h_3 h_4 h_5 h_6".split(), \
                                  "Pressure Head (mm)": [0.,0.,0.,0.,0.,0.], \
                                  "Total Head (mm)": [0.,0.,0.,0.,0.,0.], \
                                  "Volume (Liter)": [0., "-", "-", "-", "-", "-"], \
                                  "Time (sec)": [0., "-", "-", "-", "-", "-"]})

raw_data_1_3 = DataGrid(rd_1_3, \
                   editable = True, \
                   layout={"height": "180px"})
raw_data_1_3.auto_fit_columns = True

print("Test #3")
raw_data_1_3

```python jupyter={"source_hidden": true}
rd_2_2 = pd.DataFrame({"Test Section": r"h_1 h_2 h_3 h_4 h_5 h_6".split(), \
                                  "Pressure Head (mm)": [0.,0.,0.,0.,0.,0.], \
                                  "Total Head (mm)": [0.,0.,0.,0.,0.,0.], \
                                  "Volume (Liter)": [0., "-", "-", "-", "-", "-"], \
                                  "Time (sec)": [0., "-", "-", "-", "-", "-"]})

raw_data_2_2 = DataGrid(rd_2_2, \
                   editable = True, \
                   layout={"height": "180px"})
raw_data_2_2.auto_fit_columns = True

print("Test #2")
raw_data_2_2

## 9.2 CALCULATIONS

For each set of measurements, calculate the flow rate; flow velocity, velocity head, and total head,  (pressure head + velocity head).  Record your calculations in the Result Table.

### Position 1: Tapering 14° to 21°


```python jupyter={"source_hidden": true}
r_1_1 = pd.DataFrame({"Test Section": r"h_1 h_2 h_3 h_4 h_5 h_6".split(), \
                                  "Distance Into Duct (m)": [0.,0.06028,0.06868,0.07318,0.08108,0.14154], \
                                  "Flow Area (m^2)": [0.00049,0.00015,0.00011,0.00009,0.000079,0.00049], \
                                  "Flow Rate (m^3/s)": [0., 0., 0., 0., 0., 0.], \
                                  "Velocity (m/s)": [0., 0., 0., 0., 0., 0.], \
                                  "Pressure Head (m)": [0., 0., 0., 0., 0., 0.], \
                                  "Velocity Head (m)": [0., 0., 0., 0., 0., 0.], \
                                  "Calculated Total Head (m)": [0., 0., 0., 0., 0., 0.], \
                                  "Measured Total Head (m)": [0., 0., 0., 0., 0., 0.]})

results_1_1 = DataGrid(r_1_1, \
                   editable = True, \
                   layout={"height": "180px"})
results_1_1.auto_fit_columns = True

print("Test #1 \n(results_1_1)")
results_1_1

```python jupyter={"source_hidden": true}
r_1_3 = pd.DataFrame({"Test Section": r"h_1 h_2 h_3 h_4 h_5 h_6".split(), \
                                  "Distance Into Duct (m)": [0.,0.06028,0.06868,0.07318,0.08108,0.14154], \
                                  "Flow Area (m^2)": [0.00049,0.00015,0.00011,0.00009,0.000079,0.00049], \
                                  "Flow Rate (m^3/s)": [0., 0., 0., 0., 0., 0.], \
                                  "Velocity (m/s)": [0., 0., 0., 0., 0., 0.], \
                                  "Pressure Head (m)": [0., 0., 0., 0., 0., 0.], \
                                  "Velocity Head (m)": [0., 0., 0., 0., 0., 0.], \
                                  "Calculated Total Head (m)": [0., 0., 0., 0., 0., 0.], \
                                  "Measured Total Head (m)": [0., 0., 0., 0., 0., 0.]})

results_1_3 = DataGrid(r_1_3, \
                   editable = True, \
                   layout={"height": "180px"})
results_1_3.auto_fit_columns = True

print("Test #1 \n(results_1_3)")
results_1_3

```python jupyter={"source_hidden": true}
r_2_2 = pd.DataFrame({"Test Section": r"h_1 h_2 h_3 h_4 h_5 h_6".split(), \
                                  "Distance Into Duct (m)": [0.,0.06028,0.06868,0.07318,0.08108,0.14154], \
                                  "Flow Area (m^2)": [0.00049,0.00015,0.00011,0.00009,0.000079,0.00049], \
                                  "Flow Rate (m^3/s)": [0., 0., 0., 0., 0., 0.], \
                                  "Velocity (m/s)": [0., 0., 0., 0., 0., 0.], \
                                  "Pressure Head (m)": [0., 0., 0., 0., 0., 0.], \
                                  "Velocity Head (m)": [0., 0., 0., 0., 0., 0.], \
                                  "Calculated Total Head (m)": [0., 0., 0., 0., 0., 0.], \
                                  "Measured Total Head (m)": [0., 0., 0., 0., 0., 0.]})

results_2_2 = DataGrid(r_2_2, \
                   editable = True, \
                   layout={"height": "180px"})
results_2_2.auto_fit_columns = True

print("Test #1 \n(results_2_2)")
results_2_2

# 10. REPORT

Prepare your lab report for this experiment directly in this Jupyter notebook, using the cells below. Your report should include the following:

 - Table(s) of raw data
 - Table(s) of results
 - For each test, plot the total head (calculated and measured), pressure head, and velocity head (y-axis) vs. distance into duct (x-axis) from manometer 1 to 6, a total of six graphs. Connect the data points to observe the trend in each graph. Note that the flow direction in duct Position 1 is from manometer 1 to 6; in Position 2, it is from manometer 6 to 1. Be sure to label your axes and include units on your plots.
 - Comment on the validity of Bernoulli’s equation when the flow converges and diverges along the duct.
 - Comment on the comparison of the calculated and measured total heads in this experiment.
 - Discuss your results, referring, in particular, to the following:
    - energy loss and how it is shown by the results of this experiment, and
    - the components of Bernoulli’s equation ($\frac{P}{\rho g}$, $\frac{v^2}{2g}$, $z$) and how they vary along the length of the test section. Indicate the points of maximum velocity and minimum pressure.

```python
## Please run this cell after filling out the tables above to produce convenient copies of tables for your report

print("Raw Data 1-1:\n", rd_1_1, "\n")
print("Raw Data 1-2:\n", rd_1_2, "\n")
print("Raw Data 1-3:\n", rd_1_3, "\n")
print("Raw Data 2-1:\n", rd_2_1, "\n")
print("Raw Data 2-2:\n", rd_2_2, "\n")
print("Raw Data 2-3:\n", rd_2_3, "\n")
print("Results 1-1:\n", r_1_1, "\n")
print("Results 1-2:\n", r_1_2, "\n")
print("Results 1-3:\n", r_1_3, "\n")
print("Results 2-1:\n", r_2_1, "\n")
print("Results 2-2:\n", r_2_2, "\n")
print("Results 2-3:\n", r_2_3, "\n")

## You will create your plots in the notebook using the cells below
## Below is sample code for creating a basic plot using Matplotlib
## See more examples and documentation at https://matplotlib.org/stable/users/index.html

import matplotlib.pyplot as plt
import numpy as np

# Data for plotting
t = np.arange(0.0, 2.0, 0.01)
s = 1 + np.sin(2 * np.pi * t)
c = 0.5 + 0.5*np.cos(2 * np.pi * t)

fig, ax = plt.subplots()
ax.plot(t, s, label = 'sin')
ax.plot(t, c, label = 'cos')

ax.set(xlabel='time (s)', ylabel='voltage (mV)',
       title='Sample plot for demonstration')
ax.legend()
ax.grid()

#fig.savefig("test.png") #This allows you to save the plot to a file
plt.show()

# In order to avoid re-typing the data you entered above,
# you can access the data you entered into the tables above as follows:
# Select the cells you want to read
# The name of the data object is listed in parentheses just above the table above
results_1_1.clear_selection()
results_1_1.select(row1=0, column1=1, row2=5, column2=1)
# row1 refers to the top of the selection (indexing starts from 0, so the first row is 0, second row is 1, etc.)
# column1 refers to the left of the selection
# row2 refers to the bottom of the selection
# column2 refers to the right of the selection
# executing the above command selects

# Now store the values of the selected cells with a convenient variable name
# It is often useful to store data as numpy arrays to make calculations easy
distances = np.array(results_1_1.selected_cell_values)

# You can confirm that you copied the correct values by printing the values
print("Distances (m):", distances)
results_1_1.clear_selection()

# To get the Flow area from the third test in position 2:
results_2_3.clear_selection()
results_2_3.select(row1=0, column1=2, row2=5, column2=2)

flow_areas = np.array(results_2_3.selected_cell_values)
print(r"Flow Areas (m^2):", flow_areas)
results_2_3.clear_selection()

## Position 1, Test 1

## Your plotting code here ##

## Position 1, Test 2

## Your plotting code here ##

## Position 1, Test 3

## Your plotting code here ##

## Position 2, Test 1

## Your plotting code here ##

## Position 2, Test 2

## Your plotting code here ##

## Position 2, Test 3

## Your plotting code here ##