Fluid Mechanics Test 1

Concept:

Specific gravity = ρ_liquid/ρ_water

Kinematic viscosity (ν) = μ/ρ

Dynamic viscosity (μ) = νρ

where, ρ = density

Calculation:

Given:

ν = 6 cm²/s = 6 × 10^-4 m²/s

S.G. = 2 = ρ/ρ_w

⇒ ρ = SG × 1000 = 2000 kg/m³

Now,

μ = 6 × 10^-4 × 2000 = 1.2 Ns/m² = 12 poise

Important conversions:

1 Poise = 0.1 Pa.s

1 stoke = 1 cm²/s = 0.0001 m2/s

Concept:

\({\rm{Bulk\;modulus\;}}\left( K \right) = \frac{{{\rm{\Delta }}P}}{{\left( { - \frac{{{\rm{\Delta }}V}}{V}} \right)}}\)

Where, ΔP = change in pressure, \(\frac{{{\rm{\Delta }}V}}{V} = volumetric\;strain\)

Calculation:

Given:

ΔP = 150 – 95 = 55 kPa, ΔV = 0.2%

\(\therefore \frac{{{\rm{\Delta }}V}}{V} = \frac{{0.2}}{{100}}\)

\({\rm{Bulk\;modulus\;}}\left( K \right) = \frac{{{\rm{\Delta }}P}}{{\left( { - \frac{{{\rm{\Delta }}V}}{V}} \right)}}\)

\(K = \frac{{55\; \times \;{{10}^3}}}{{\left( {\frac{{0.2}}{{100}}} \right)}}\)

K = 275 × 10⁵

∴ K = 27.5 MPa

Concept:

Capillary rise,

\(h = \frac{{4\sigma \cos \theta }}{{\rho gd}}\)

Calculation:

For water: σ = 0.0735 N/m (given)

θ = 0° , ρ = 1000 kg/m³, g = 9.81 m/s²

\(\therefore h = \frac{{4 \times 0.0735 \times \cos 0}}{{1000 \times 9.81 \times 6 \times {{10}^{ - 3}}}}\)

h = 4.979 mm

∴ h = 4.98 m