Pressure drop calculations

Department of Mechanical Engineering
College of Engineering, Pune (COEP)
Forerunners in Technical Education
1
Heat Exchanger Pressure Drop Analysis
P. R. Dhamangaonkar
Ref: Fundamentals of Heat Exchanger Design,
By Ramesh K. Shah and Dušan P. Sekulic

2
• Fluids need to be pumped through the heat exchanger in most
applications.
• The fluid pumping power is proportional to the fluid pressure drop,
which is associated with fluid friction and other pressure drop
contributions along the fluid flow path.
• The fluid pressure drop has a direct relationship with exchanger heat
transfer, operation, size, mechanical characteristics, and other factors,
including economic considerations.

3
The determination of pressure drop Δp in a heat exchanger is essential
for many applications
• This pumping power is proportional to the exchanger pressure drop
• Saturation temperature changes with changes in saturation pressure
and in turn affects the temperature potential for heat transfer.
Importance of Pressure Drop

4
Let us first determine the relative importance of the fluid pumping
power P for gas flow vs. liquid flow in a heat exchanger.
P is proportional to Δp in a heat exchanger and is given by
Where is the is volumetric flow rate and ηp is the pump/fan
efficiency.
G= core mass velocity=ρum
Ao= minimum free flow area
and f is the Fanning friction factor

5
Where f=0.046 Re-0.2 for fully developed turbulent flow
If the flow rate and flow passage geometry are given, to determine the order of
magnitude for the fluid pumping power requirement for gas vs. liquid flow , it is
evident that
Dependence of Power

6
Fluid Pumping Devices
The most common fluid pumping devices are fans, pumps, and
compressors.
A fan is a low-pressure air- or gas-moving device, which uses rotary
motion.
There are two major types of fans: depending on the direction of flow
through the device.
Fans may be categorized as blowers and exhausters.
A pump is a device used to move or compress liquids.
A compressor is a high-volume centrifugal device capable of
compressing gases
Blower: (500 Pa or 2.0 in. H2O)
Compressor: 100 to 1500 kPa (15 to 220 psi) and higher

7
Fans and pumps are volumetric devices and are commonly used to
pump fluids through heat exchangers.
This means that a fan will develop the same dynamic head [pressure
rise per unit fluid (gas) weight across the fanj6] at a given capacity
(volumetric flow rate) regardless of the fluids handled, with all other
conditions being equal.
The head, dynamic head or velocity head is referred to as the kinetic
energy per unit weight of the fluid pumped, expressed in units of
millimeters or inches (feet).
Thus the pressure rise across a fan (which is mainly consumed as the
pressure drop across a heat exchanger) can be expressed in terms of
the head H as follows:

8
Major Contributions to the Heat Exchanger Pressure Drop
The pressure drop associated with a heat exchanger is considered as a
sum of two major contributions:
• pressure drop associated with the core or matrix,
• pressure drop associated with fluid distribution devices
Ideally most of the pressure drop available should be utilized in the
core and a small fraction in the manifolds, headers, or other flow
distribution devices.
But for plate heat exchangers and other heat exchangers the pressure
drop associated with manifolds, headers, nozzles, and so on, may not
be a small fraction of the total available pressure drop.
If core pressure drop > manifold and header pressure drops,
relatively uniform flow distribution through the core is obtained.

9
The flow distribution through the core is uniform.
The core pressure drop is determined separately on each fluid side.
(1) frictional losses associated with fluid flow over the heat transfer
surface (this usually consists of skin friction plus form drag),
(2) momentum effect (pressure drop or rise due to the fluid density
changes in the core),
(3) pressure drop associated with sudden con-traction and expansion
at the core inlet and outlet, and
(4) gravity effect due to the change in elevation between the inlet and
outlet of the exchanger. (negligible for gases)

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For vertical liquid flow through the exchanger, the pressure drop or
rise due to the elevation change is given by
Where,
- the ‘‘+’’ sign denotes vertical up flow (i.e., pressure drop),
- the ‘‘-’’ sign denotes vertical down flow (i.e., pressure rise or
recovery),
-‘g‘ is gravitational acceleration,
- L is the exchanger length,
- ρm is the mean fluid mass density calculated at bulk temperature and
mean pressure between the two points.

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Assumptions for Pressure Drop Analysis
1. Flow is steady and isothermal, and fluid properties are independent of
time.
2. Fluid density is dependent on the local temperature only or is treated as
a constant (inlet and exit densities are separately constant).
3. The pressure at a point in the fluid is independent of direction. If a
shear stress is present, the pressure is defined as the average of normal
stresses at the point.
4. Body forces are caused only by gravity (i.e., magnetic, electrical, and
other fields do not contribute to the body forces).
5. If the flow is not irrotational, the Bernoulli equation is valid only along
a stream-line.
6. There are no energy sinks or sources along a streamline; flow stream
mechanical energy dissipation is idealized as zero.
7. The friction factor is considered as constant with passage flow length.

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Extended Surface Heat Exchanger Pressure Drop
Plate-Fin Heat Exchangers
Δp=Δp1-2 +Δp2-3 –Δp3-4
TheΔp1-2 is the pressure drop at the
core entrance due to sudden
contraction,
TheΔp2-3 is the pressure drop with in the core and referred as core
pressure drop.
TheΔp3-4 is the pressure rise at the core exit.

13
Core Pressure Drop.
The pressure drop within the core:
(1) the pressure loss caused by fluid friction,
(2) the pressure change due to the momentum
rate change in the core.
Consider a differential element of flow length dx in the core
Considering Various force and momentum rate terms in and out of
this element
τw is the effective wall shear stress due to skin friction, form drag, and
internal contractions and expansions, if any.
P is the wetted perimeter of the fluid flow passages

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Rearranging and simplifying
Fanning friction factor f is the ratio of wall shear stress τw to the flow
kinetic energy per unit volume.

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Force and momentum rate terms for a differential element of a heat exchanger core
• While τwPdx is shown acting on both top and bottom surface in
reality it acts along the entire surface Pdx
• τw is dependent on the flow passage geometry and size, fluid velocity,
fluid density and viscosity, and surface roughness, if any
• The minimum free-flow area Ao is constant in most heat exchangers
• The friction factor, f , is derived experimentally for a surface or
derived theoretically for laminar flow and simple geometries

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τw = the effective wall shear stress
ρ = fluid mass density determined at the local bulk temperature and
mean pressure
rh = fluid mass density determined at the local bulk temperature and
mean pressure
= (Ao /P)
Dh = hydraulic diameter = 4rh
Using d(1/ρ)= -(1/ρ2)

17
Integrating from x=0 (ρ=ρi , p=p2) to x=L (ρ=ρo , p=p3)
Where mean specific volume
For a liquid with any flow arrangement, or for an ideal gas with C*=1
and any flow arrangement except for parallel flow,
v = the specific volume in m3/kg

18
In general,
(1/ρ)m ≈(1/ρm) is a good approximation for liquids with very minor
changes in density with temperatures and small changes in pressure.
For a perfect gas with C*=0 and any exchanger flow arrangement,

19
The core pressure drop has two contributions:
1. The first term represents the momentum rate change or the flow
acceleration (deceleration) effects due to the fluid heating
(cooling);
- Its positive value represents a pressure drop for flow acceleration
and the negative value a pressure rise for flow deceleration.
2. The second term represents the frictional losses and is the
dominating term for Δp.

20
Core Entrance Pressure Drop
The core entrance pressure drop consists of two contributions:
(1) the pressure drop due to the flow area change, and
(2) the pressure losses associated with free expansion that follow
sudden contraction.
Assumption:
The temperature change at the entrance is small and that the fluid
velocity is small compared to the velocity of sound. Thus the fluid is
treated as incompressible.
The pressure drop at the entrance due to the area change alone, for a
frictionless incompressible fluid, is given by the Bernoulli equation.

21
Where ρi is the fluid density at the core inlet and ρi =ρ1 =ρ2 and ρ’2 is
the hypothetical static pressure at section 2 if the pressure drop would
have been alone due to the area change.
The continuity equation gives, ρi A0,1 u1 =ρi A0,2 u2
Let,

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the pressure drop at the core entrance due to the area change alone,
The second contribution to the pressure drop at the entrance is due to
the losses associated with irreversible free expansion that follows the
sudden contraction.
Pressure drop due to these losses= contraction loss coefficient Kc X
the dynamic velocity head at the
core inlet
Kc is a function of the contraction ratio σ, Reynolds number Re, and flow cross-
sectional geometry.

23
Entrance and exit pressure loss
coefficients for
(a) a multiple circular tube core,
(b) multiple-tube flat-tube core,
(c) multiple square tube core, and
(d) multiple triangular tube core
with abrupt contraction (entrance)
and abrupt expansion (exit).
(From Kays and London, 1998.)

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Kc is made up of two contributions:
1. irreversible expansion after the vena contracta and
2. the momentum rate change due to a partially or fully developed
velocity profile just downstream of the vena contracta.

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Core Exit Pressure Rise
The core exit pressure rise (p4-p3) is divided into two contributions
1. the pressure rise due to the deceleration associated with an area
increase
2. The pressure loss associated with the irreversible free expansion
and momentum rate changes following an abrupt expansion
The first contribution
The second contribution
The exit loss coefficient Ke is based on the dynamic velocity head at the core outlet. It
is function of function of the expansion ratio, the Reynolds number and the flow
cross-sectional geometry.

26
The definition of Ke considers two effects:
(1) Pressure loss due to the irreversible free expansion at the core exit,
and
(2) Pressure rise due to the momentum rate changes, considering
partially or fully developed velocity profile at the core exit and
uniform velocity profile far downstream at section 4
Hence, the magnitude of Ke will be positive or negative,

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Total Core Pressure Drop.
The total core pressure drop on one fluid side of a plate-fin exchanger
is given by :
Δp = Δp1-2+Δp2-3-Δp3-4

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The core frictional pressure drop, being the major contribution in the
total core pressure drop may be approximated as follows in different
forms:
Corresponding fluid pumping power P is

Pressure drop calculations

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