<jupyter_start><jupyter_text>Table of Contents 1. (hand in camera upload or on paper):  Integrate $Z=\int D^6 n(D) dD$  assuming a Marshall Palmer size distribution and show that it integrates to:      $$Z \approx 300 RR^{1.5}$$   with Z in $mm^6\,m^{-3}$ and RR in mm/hr.  It's helpful to know that:      $$\int^\infty_0 x^n \exp( -a x) dx = n! / a^{n+1}$$<jupyter_code>def findPr(Z,K2,La,R,R1=None,Pt=None,b=None,Z1=None):
   """
    solve stull eqn 8.23
    
    Parameters
    ----------
    
    input: Z (mm^6/m^3), K2 (unitless), La (unitless),R (km)
           plus radar coefficients appropriate to given radar (like Nexrad)
           
    Returns
    -------
    
    Pr in W 
   """ 
   # YOUR CODE HERE
   raise NotImplementedError()

from numpy.testing import assert_almost_equal
#stull p. 246 sample appliation
# given

#coefficents for nexrad
R1=2.17e-10#range factor, km, Stull 8.25
Pt=750.e3 #transmitted power, W, stull p. 246
b=14255 #equipment factor, Stull 8.26

nexrad=dict(R1=R1,Pt=Pt,b=b)

Z=1.e4  #Z of 40 dbZ
R=20    #range of 20 km
K2=0.93  #liquid water
La=1   #no attenuation

power_watts=findPr(Z,K2,La,R,**nexrad)
assert_almost_equal(1.17e-8,power_watts)<jupyter_output><empty_output>
{'fraction_non_alphanumeric': 0.14391447368421054, 'fraction_numerical': 0.055098684210526314, 'mean_word_length': 3.15358361774744, 'pattern_counts': {'":': 0, '<': 5, '<?xml version=': 0, '>': 5, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'chain_length': '1', 'dir': 'jupyter-structured-clean-dedup', 'id': '13794', 'license': 'MIT', 'n_tokens_mistral': 526, 'n_tokens_neox': 473, 'n_words': 134, 'path': 'assignments/radar_probs13.ipynb', 'repo_name': 'Pearl-Ayem/ATSC_Course_Work', 'size': '1216'}