Head loss due to friction
The objective :
1. To determine the head loss and friction factor for laminar & turbulent flow in a smooth pipe over a range of Reynolds's number .
2. To obtain the following relationships :
a. Head loss as a function of the velocity of flow .
b. Friction factor as a function of Reynolds number .
Theory :
The friction resistance to the flow of fluid through a pipe results in a loss of pressure energy for a given fluid flowing a long a given pipe, experiments show that for laminar flow :
Hl α V
And for turbulent flow :
Hl α Vn
Where :
Hl :is the loss of pressure head .
V : the mean velocity of flow . n : an index that lies between ( 1.7 – 2.0 ) depending on Reynolds number ( Re ) and on the roughness of the pipe wall.
The Reynolds number ( Re ) is given by :
Re = ( ρ.V.d /μ) ------------------ ( 1 )
Where : d = pipe diameter
Ρ = fluid density μ = absolute viscosity
In engineering practice, it is customary to use Darcy's equation to express the pressure head loss as follows : hL = h 1 – h 2 = 4 ( L / d ) ( V2 / 2g ) ---------------- ( 2 )
Where : h1 & h2 : static heads at two points in the pipe
L = distance between h1 & h2 f = fexp.: experimental friction factor which varies with Re and pipe roughness .
Blasius has shown that a line whose equation is may closely approximate the friction factor Reynolds's number relationship for turbulent flow : ftheo. = ( 0.079 /Re0.25 ) -----------------------( 3 )
For laminar flow condition ,the Hagen-Poiseurlle law yields the relation : ftheo. = ( 16 / Re ) ----------------------- ( 4 )
Apparatus :
The laminar / turbulent pipe flow apparatus consist of a circuit through which the fluid is circulated continuously by means of gear pump .the selected fluid is oil of a suitable viscosity to give values of Re well down into the laminar region. It is drawn from the reservoir and delivered by way of the lower horizontal pipe to the Perspex –
1. To determine the head loss and friction factor for laminar & turbulent flow in a smooth pipe over a range of Reynolds's number .
2. To obtain the following relationships :
a. Head loss as a function of the velocity of flow .
b. Friction factor as a function of Reynolds number .
Theory :
The friction resistance to the flow of fluid through a pipe results in a loss of pressure energy for a given fluid flowing a long a given pipe, experiments show that for laminar flow :
Hl α V
And for turbulent flow :
Hl α Vn
Where :
Hl :is the loss of pressure head .
V : the mean velocity of flow . n : an index that lies between ( 1.7 – 2.0 ) depending on Reynolds number ( Re ) and on the roughness of the pipe wall.
The Reynolds number ( Re ) is given by :
Re = ( ρ.V.d /μ) ------------------ ( 1 )
Where : d = pipe diameter
Ρ = fluid density μ = absolute viscosity
In engineering practice, it is customary to use Darcy's equation to express the pressure head loss as follows : hL = h 1 – h 2 = 4 ( L / d ) ( V2 / 2g ) ---------------- ( 2 )
Where : h1 & h2 : static heads at two points in the pipe
L = distance between h1 & h2 f = fexp.: experimental friction factor which varies with Re and pipe roughness .
Blasius has shown that a line whose equation is may closely approximate the friction factor Reynolds's number relationship for turbulent flow : ftheo. = ( 0.079 /Re0.25 ) -----------------------( 3 )
For laminar flow condition ,the Hagen-Poiseurlle law yields the relation : ftheo. = ( 16 / Re ) ----------------------- ( 4 )
Apparatus :
The laminar / turbulent pipe flow apparatus consist of a circuit through which the fluid is circulated continuously by means of gear pump .the selected fluid is oil of a suitable viscosity to give values of Re well down into the laminar region. It is drawn from the reservoir and delivered by way of the lower horizontal pipe to the Perspex –