Fluid Friction Measurements

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  • Topic: Fluid dynamics, Piping, Volumetric flow rate
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FLUID FRICTION MEASUREMENTS
YEDITEPE UNIVERSITY DEPARTMENT OF MECHANICAL ENGINEERING

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YEDITEPE UNIVERSITY ENGINEERING FACULTY MECHANICAL ENGINEERING LABORATORY

Fluid Friction Measurements
1. Objective: Ø To determine the head loss. Ø To determine the head loss associated with flow of water through standard fittings used in plumbing installations. Ø To determine the relationship between friction coefficient and Reynolds’ number for flow of water through a pipe having a roughened bore. Ø To determine the water velocity by using flow measurement devices. 2. Equipment:

The test pipes and fittings are mounted on a tubular frame carried castors. Water is fed in from the hydraulics bench via the barbed connector (1), and is fed back into the volumetric tank via the exit tube (23). · · · · · · · · · · · · · · An in-line strainer (2) An artificially roughened pipe (7) Smooth bore pipes of 4 different diameter (8), (9), (10) and (11) A long radius 90° bend (6) A short radius 90° bend (15) A 45° “Y” (4) A 45° elbow (5) A 90° “T” (13) A 90° mitre (14) A 90° elbow (22) A sudden contraction (3) A sudden enlargement (16) A pipe section made of clear acrylic with a Pitot static tube (17) A Venturi made of clear acrylic (18) 2

· · · ·

An orifice meter made of clear acrylic (19) A ball valve (12) A globe valve (20) A gate valve (21)

3. Theory: 3.1 Fluid Friction in a Smooth Bore Pipe Two types of flow may exist in a pipe: 1) Laminar flow at low velocities where h ∝ V 2) Turbulent flow at higher velocities where h ∝ V n where h the head loss due to friction, V the fluid velocity, and 1.7 < n < 2.0. These two types of flow are separated by a transition phase where no definite relationship between h and V exists. Laminar

Transient

Turbulent

The friction factor, λ , is defined as,

∆h =
where
∆h L D V

λ⋅L V2 ⋅ D 2⋅ g

the head loss [m] the length between the tapping [m] the diameter of the pipe [m] the mean velocity [m/s]

The Reynolds’ number, Re, can be found using the following equation: ρ ⋅V ⋅ D Re = µ where µ dynamic viscosity (1.15 x 10 −3 Ns/m at 15°C) ρ the density (999 kg/m 3 at 15 o C)

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For a pipe with a circular cross sectional area; Laminar Flow Re < 2000 Transitional Flow 2000 < Re < 4000 Turbulent Flow Re > 4000 Having established the value of Reynolds’ number for flow in the pipe, the value of f may be determined using a Moody diagram, a simplified version of which is shown below.

3.2 Head Loss Due to Pipe Fittings The local loss can be estimated as follows;

∆h (mH 2 O ) =
where K V g

K ⋅ V2 2⋅g

the fitting “loss factor”, the mean velocity of water through the pipe [m/s] the acceleration due to gravity [m/s2].

The loss factor is dimensionless and is a function of Reynolds number. In the standard literature, the loss factor is not usually correlated with Re and roughness but simply with its geometry and the diameter of the pipe, implicitly assuming that the pipe flow is turbulent.

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3.3 Flow Measurement Orifice plate, venturi and a pitot tube will be used to measure the water flow rate. For an orifice plate or Venturi, the flow rate and differential head are related by Bernoulli’s equation with a discharge coefficient added to account for losses; 2 ⋅ g ⋅ ∆h Q = C d ⋅ Ao ⋅ ( Ao A1 )2 − 1 where Q the flow rate [m³/s], Cd the discharge coefficient (Cd = 0.98 for a Venturi, 0.62 for an orifice plate), A0 the area of the throat or orifice in m² (d0 = 14mm for the Venturi, 20mm for the orifice plate), A1 the area of the pipe upstream m² (d1 = 24mm), the differential head of water [m], ∆h g the acceleration due to gravity [m/s²]. For a Pitot tube, the differential head measured between the total and static tappings is equivalent to the velocity head of the fluid; V2 = h1 − h2 2⋅ g

V = 2 ⋅ g ⋅ (h1 − h2 )
where
V (h1 − h2 ) g

the mean velocity of water through the pipe [m/s], the differential head of water [m], the acceleration due to gravity [m/s²].

3.4...
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