## Chapter 6 : Dimensional Analysis and Dynamic Similitude¶

### Example 6.2 Page no 233¶

In [3]:
# Velocity of the flow

# Given

L = 10                          # length scale lp/l

# crue oil at 20 deg C

rhop = 0.86*998.2                 # density inn kg/m**3

mup = 8*10**-3                    # viscosity in Ns/m**2

Vp = 2.5                          # Velocity in m/s

# water at 20 deg C

rhom = 998.2                     # density in kg/m**3

mum = 1.005*10**-3               # viscosity in Ns/m**2

# Solution

Vm = Vp*L*(rhop/rhom)*(mum/mup)  # velocity in m/s

print "Hence the model should be tested at a velocity of ",round(Vm,2),"m/s. This velocity in the model is called corresponding velocity"

Hence the model should be tested at a velocity of  2.7 m/s. This velocity in the model is called corresponding velocity


### Example 6.3 Page no 233¶

In [1]:
# Mximum head on the crest and corresponding discharge for dynamically similar conditions

# Given

from __future__ import division

from math import *

l = 300                               # length in ft

Q = 100000                            # discharge in cfs

Cd = 3.8                              # coefficient of discharge

L = (1/50)                              # length scale

# Solution

Qm = 100000*(L)**(5/2)                     # model discharge in cfs

print "Maximum discharge, Qm = ",round(Qm,8),"cfs"

H = (Q/(Cd*l))**(2/3)                 # height over spill way

h = H*L*12                              # head over spill model

print "Maximum head over crest = ",round(h,2),"ft"

Maximum discharge, Qm =  5.65685425 cfs
Maximum head over crest =  4.74 ft

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