Question
- The velocity of propagation, c of surface waves is assumed to depend on the water depth, y, the water density, ?, and the acceleration due to gravity, g. Express these variables as a dimensionless group.
The velocity of propagation, c of surface waves is assumed to depend on the water depth, y, the water density, ?, and the acceleration due to gravity, g. Express these variables as a dimensionless group. The velocity of propagation, c of surface waves is assumed to depend on the water depth, y, the water density, ?, and the acceleration due to gravity, g. Express these variables as a dimensionless group. The velocity of propagation, c of surface waves is assumed to depend on the water depth, y, the water density, ?, and the acceleration due to gravity, g. Express these variables as a dimensionless group. The velocity of propagation, c of surface waves is assumed to depend on the water depth, y, the water density, ?, and the acceleration due to gravity, g. Express these variables as a dimensionless group. The velocity of propagation, c of surface waves is assumed to depend on the water depth, y, the water density, ?, and the acceleration due to gravity, g. Express these variables as a dimensionless group. The velocity of propagation, c of surface waves is assumed to depend on the water depth, y, the water density, ?, and the acceleration due to gravity, g. Express these variables as a dimensionless group.
Explanation / Answer
c=[LT^(-1)]
y=[L]
p=[ML^-3]
g=[LT^-2]
let us consider the dimensionless group,
G= c^a * y^b *p^c * g
G is dimensionless....
summing up powers of L to zero gives,
a+b-3c+1=0-----(1)
summing up powers of T to zero,
-a-2=0------(2)
for M,
c=0-----(3)
from (2),
a= -2
from (3),
c=0
from (1),
B=1
G= gy/(c^2)
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