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## Homework Statement

A body when tested in air of density 1.18 kg/m3 and dynamic viscosity 1.52x10^-5 Pas at a velocity of 35 m/s was found to produce a resistance of 250 N. A similarly shaped body 10 times longer than the original was tested in water of dynamic viscosity 1x10^-3 Pas. Determine the resistance for the larger body.

## Homework Equations

In the previous question I have obtained via the Pi-theorem:

R / (rho x l^2 x v^2) = f ((rho x v x l)/μ)

which is correct.

## The Attempt at a Solution

1:

rho air = 1.18 kg/m3

μair = 1.52x10^-5 Pas

v = 35 m/s

R = 250N

l

2:

rho water = 1000 kg/m3

μwater = 1x10^-3 Pas

v = ?

R = ?

10l

For dynamic similarity:

(rho1 x v1 x l1)/μ1 = (rho2 x v2 x l2)/μ2

(1.18 x 35 x l)/1.25x10^-5 = (1000 x v2 x 10l)/1x10^-3

(1.18 x 35)/1.25x10^-5 = (1000 x v2 x 10)/1x10^-3

I get: v2 = 0.2717 m/s

Complete similarity:

R1 / (rho1 x (l^2)1 x (v^2)1) = R2 / (rho2 x (l^2)2 x (v^2)2)

250 / (1.18 x l^2 x 35^2 = R2 / (1000 x 100l^2 x 0.2717^2)

250 / (1.18 x 35^2 = R2 / (1000 x 100 x 0.2717^2)

I get: R2 = 1276.8 N

Though the answer should be:

R2 = 1082063.71 N

Does anyone know what I am doing wrong?

Thanks in advance!