How can you prove that v is equal to square root of gh using diamensional analyasis
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Answer:
According to given
V=kp
a
ρ
b
{p=pressure,ρ=density}
Applying dimensional formula on both sides
[LT
−1
]=K[ML
−1
T
−2
]
a
[ML
−3
]
b
On comparing dimension of M,L and T
a+b=0−(1)
−a−2b=0−(2)
a=
2
1
−(3)
From equation(3)
a=
2
1
From equation(i) and (ii)
b=
2
−1
Hence,
v=kp
2
1
ρ
−
2
1
v= √ρ/p
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