Fluid Mechanics Lab Manual

REYNOLD’S APPARATUS Aim To study different types of flow and to determine the Reynold’s number. Theory In Reynold’s experiments, the ration of inertial to viscous forces was observed to be dimensionless and related to viscosity, average pipeline velocity and geometrically similar boundary conditions. For a homogeneous Newtonian fluid, this dimensionless ration is Re expressed as Re

=

ρDV/µ (dimensionless)

ρ

=

density of fluid (kg/m3)

V

=

Velocity of fluid (m/s)

D

=

Diameter of glass tube (m)

µ

=

Viscosity of fluid (NS/m2)

For, NRe < 2100 – Laminar flow NRe > 4000 – Turbulent flow 2100< NRe 1000) 8.

experimental friction factor f p = ∆P фs DP ε3 / ρ V2l (1- ε)

9.

pressure drop per unit length of bed ∆P /l = h x (0.8853) (N/m2)

DATA D = 0.05m SP=4.95 x10-4 m3 g = 9.81m/s2 ρ= 1000kg/ m3 DP= 0.00847m

A= 1.964 x 10-3 m2 do = 0.009m di = 0.006m LP=0.009m L = 0.36m

ε =0.66 μ = 8.29 x 10-4 Ns/ m2

фs=0.455

OBSERVATION Sl No Rotameter reading LPH

Full length h (mm)

Half length h(mm)

Forward

Forward

Reverse

Reverse

1 2 3

8 9 10

CALCULATION TABLE Sl No

Q

V

Re

m/s

MODEL CALCULATION

RESULT

fr

Fp(half)

Fp(full)

∆P/l(half)

∆P/l(full)

Pressure drop per unit length of the bed was calculated Plotted the log –log graph for friction factor and modified Reynolds number REASONING

FLUIDISED BED APPARATUS

AIM To study the flow through fluidized bed and tom determine pressure drop per unit length of bed. THEORY Fluidization is one of the methods available for contacting granular solids with fluids. A fluidized bed provides a higher interfacial surface area of contact of higher transfer rates .When a fluid is passed upward through bed of solids ,there will be certain pressure drop across the bed to maintain the fluid flow .Depending up on the bed geometry , fluid velocity and particle characteristics the following phenomenon occurs with gradual increase in fluid velocity . At law velocities there is a pressure drop across the bed but the solid bed is static (curve AB) as the fluid velocity is reached the bed starts expanding .At this point the pressure drop across the bed equals to the mass per unit area of the bed .This point is known as point of incipient fluidization .Once the particle are separated , pressure require to maintain fluidization is less. As the velocity is further increased ,the pressure drop remains constant until the bed assume a loosest form of packing If froude’s number , f >1 aggregative fluidization .f < 1 particulate fluidization Pressure drop across a fixed bed is given by Erguns equation ∆Pε Dp/ ρL(1-ε)V2

= 150 (1-ε)µ/ DpVp ------------------1

. ε =ZA – WS/ρ /ZA= 1- WS/ZAρ At the onset of fluidization pressure drop across the bed equals the weight or bed per unit area of cross section. ∆P/z = ρ(ρp- ρ)( 1-ε)-----------------------3 From equation 1 and 3 The minimum fluidization velocity Vmf = Dp2g (ρp- ρ) ε3mf / 150(1- εmf ) µ Fluidization efficiency = GF-Ge/ Ge

Porosity of static bed Take some solids in a granulated cylinder and note it’s initial volume (v1). Add a known volume (v2) of water & note the final volume. The porosity of static bed is given by, ε0 =V1+V2-V3/V1 PROCEDURE Note height of bed in column .start with minimum flow of water in the column at a constant rate .Note the flow rate ,bed height(z) and pressure drop across the column after the steady state is reached .Gradually increase the flow rate of water steadily and repeat the above step for 8-10 different rate of flow continue till the bed is fluidized and finally becomes turbulent.(ie, there is no appreciate change in pressure drop indicated by manometer .)Now decrease the flow rate back to zero and record the same data. FORMULAE Velocity of water =v = Q x 10-3/3600A Pressure drop per unit length of bed ∆P/Z = h x 9.81N/m3 Porosity of fluidized bed ε = 1-z0/z1 (1- ε0) Wen and Yu equation (NRe)mf =(A2+BNar)1/2-A Nar = (dp) 3 x ρH2O (Pρ- ρH2O) ρ /µH2O2 OBSERVATION SL Q (LPH) No

Forward Z(cm)

1 2 3 9 10

reverse h(mm)

Z(cm)

h(mm)

CALCULATION TABLE Sl No Flow Height(10-2m) V m/s rate Q m3/s forward reverse

Pressure drop, Porosity (ε) NRe ∆P/z (N/m2) forward reverse forward reverse

1.

RESULT Minimum fluidization velocity from Pressure drop curve for forward =

m/s

Minimum fluidization velocity from Pressure drop curve for reverse =

m/s

Minimum fluidization velocity from porosity graph

=

Minimum fluidization velocity from Wen & Yu equation REASONING

DRAG COEFFICIENT AIM • • •

•

To study the drag coefficient of a falling sphere for the given fluid To determine the settling velocity of particle for the given fluid To plot graph for logarithmic Reynold’s number vs logarithmic CD To verify the stok’s law

=

THEORY When a sphere falls through a liquid at terminal settling velocity , the drag coefficient can be determined as a function of NRe .At law NRe , Stoke’s law prevails as the initial forces are negligible and drag is a function of viscosity When the particle is at a sufficient distance from the boundary of the containers and from all other particle (no particle or solid boundary should be either 20 times the diameter of the particle ), so that is motion is not affected by them,the process is called free settling .Now the forces acting on the particle are the gravitational force, buoyant force and the drag force .The resultant force on the particle is equal to fg-fb- fd.At terminal settling velocity ,the resultant force are equal to zero. CD = 4 DP (lp-l1)g / 3Ut2 l1 Ut = g DP2 (lp-l1) / 18µ At low Reynold’s no ie, NRe