Dr. Nikos J. Mourtos AE 160 Aerodynamic Forces
DEFINE
A flat plate is flying supersonically at an angle-of-attack. The flow field is illustrated in
the figure below. Because there is no upstream influence in supersonic flow, the
conditions on the upper an

Dr. Nikos J. Mourtos AE 160 / ME 111
MOMENTUM (Newtons 2nd Law of Motion)
Case 5 Thrust Reverser
Figure 1 Schematic of a jet engine thrust reverser deployed.
We have seen how a propeller and a turbofan engine generate thrust in one direction by
accelerati

Dr. Nikos J. Mourtos AE 160 / ME 111
MOMENTUM (Newtons 2nd Law of Motion)
Case 6 Toy Car
Consider a toy car moving at a constant speed uc , propelled by a water gun as shown in
Figure 1. The water jet speed is u j and remains constant, the jet cross-secti

Dr. Nikos J. Mourtos AE 160
FLOW RATE (Discharge)
Example: Flow through rectangular channel
Water flows through a rectangular channel as shown. The channel width is 1.5
m. Find the discharge in the channel.
Assumptions:
1. Steady flow
2. Incompressible fl

VISCOSITY Example Problem: Rotating Cone A solid cone is rotating with initial angular velocity 0 inside a conical seat, as shown in the figure. The clearance h is filled with oil of viscosity . Derive an expression for the time required to reduce the con

Dr. Nikos J. Mourtos AE 160 / ME 111
MOMENTUM (Newtons 2nd Law of Motion)
Case 7 Rocket
Figure 1 Schematic of a rocket accelerating vertically.
A rocket has just lifted off the ground and is accelerating vertically. The following is
known:
The instantane

AE 160 / ME 111 Dr. Nikos J. Mourtos Fluid Properties (Viscosity)
Workout Problem:
Rotating Disk
A thin layer of viscous oil separates a rotating disk from a solid surface, as shown in the
figure.
a. If the disk is rotated @ ! = 1 rad / s , what is the ra

AE 160 / ME 111 Dr. Nikos J. Mourtos Fluid Properties (Viscosity)
Example Problem:
Rotating Disk
A disk rotates inside an oil bath, as shown in the figure. The clearance is filled with oil.
Derive an expression for the viscous torque on the disk.
Given
Di

Boundary Layers / Skin - Friction Drag
Example Problem: The skin-friction drag of an airplane wing.
Calculate the skin-friction drag of the Wright Flyer I wings.
Note: The Wright Flyer I is a biplane.
Given:
flight speed:
atmospheric conditions:
wing span

Dr. Nikos J. Mourtos AE 160 / ME 111 / ME 223
BOUNDARY LAYERS
Example: Calculate flow velocity at a point inside a LBL
A liquid flows past a smooth flat plate. Calculate the flow velocity 1 m from the LE and
1 mm from the surface.
Given:
Flow speed:
u = 1

Dr. Nikos J. Mourtos AE 160
BOUNDARY LAYERS
Example: Skin Friction Drag of an Airplane Wing
The following information is given about the Shorts 330 airplane:
Wing planform area
Wing span:
Cruising speed:
Cruising altitude:
S = 42.10 m 2
b = 22.76 m
V = 30

Dr. Nikos J. Mourtos AE 160 / ME 111 / ME 223
BOUNDARY LAYERS
Example: Calculate flow velocity at a point inside a TBL
Water at 100C flows with velocity 6 m/s past a flat plate. At a particular section
downstream of the LE of the plate, the BL is turbulen

AE160 Aerodynamics I
Team Members:
Prof. Rachael Ishaya
Fall 2016
Date:
Fluid Properties Workout Problem 1
Consider the pipe and the cylinder of the example problem done in class. However, in this case,
the cylinder in now slowing down as it falls. At a p

Lecture 9: Equivalent Force-Couples (3D)
Trusses
A truss is a rigid frame work usually
consists of beams, struts and bars to
resist deformation due to loads
In aircraft this type of frame work is
mainly used for fuselage and wings.
The truss constr

Dr. Nikos J. Mourtos AE 160 / ME 111
MOMENTUM (Newtons 2nd Law of Motion)
Case 2 Turbofan Engine
Figure 1 The GE 90 turbofan engine, which powers the Boeing 777.
Figure 2 The Pratt & Whitney JT9 engine, which powers the Boeing 747 (from
<http:/commons.wik

Dr. Nikos J. Mourtos AE 160 / ME 111
MOMENTUM (Newtons 2nd Law of Motion)
Case 4.1 Unsteady Water Pipe Flow
Consider water flow in a straight, horizontal pipe. Imagine the valve, which controls the
flow, is slowly turned on, increasing the flow rate throu

Dr. Nikos J. Mourtos AE 160 / ME 111
Momentum (Newtons 2nd Law of Motion)
Case 3 Airfoil Drag
A very important application of Momentum in aerodynamics and hydrodynamics is the
calculation of the drag of a body by calculating the momentum loss in its wake

Dr. Nikos J. Mourtos AE 160 / ME 111 Bernoullis Equation
Example Problem: Vertical Water Jet
Find the diameter of the jet at a point 5 m above the nozzle.
Given:
Nozzle exit diameter:
Jet velocity at nozzle exit:
d0 = 0.025 m
V0 =15 m/sec
Assumptions:
1.

Dr. Nikos J. Mourtos AE 160 Aerodynamic Forces
DEFINE
A flat plate is flying subsonically at an angle-of-attack. The flow field and the pressure
distribution around the plate are illustrated in the figures below.
Given:
Free stream conditions: sea level,

Dr. Nikos J. Mourtos AE 160
CONTINUITY
Example: Flow through the Cylinder of a Piston-Engine
A piston is moving up during the exhaust stroke of a 4-cycle engine. Determine
the rate at which the density of the mixture is changing in the cylinder.
Given:
Bo

Dr. Nikos J. Mourtos AE 160 / ME 111 Bernoullis Equation
Example Problem: Hydrofoil
When testing a hydrofoil the minimum pressure on its surface was found to be 70 kPa-a
when the foil was submerged 1.8 m and towed at a speed of 7 m/sec.
(a) At the same de

Dr. Nikos J. Mourtos AE 160
CONTINUITY
Example: Flow through a Solid-Propellant Rocket-Engine
Determine the rate at which propellant is being consumed in the combustion
chamber of the solid-propellant rocket engine shown in the figure.
Given:
Combustion c

Dr. Nikos J. Mourtos AE 160 Continuity
Workout: Wind Tunnel with Porous Walls
The wind tunnel shown below has a porous test section, to allow for boundary layer
suction. Wall suction significantly reduces the thickness of the boundary layer and
allows for

AE 160 / ME 111 Dr. Nikos J. Mourtos Flow Similarity
Define
The pressure rise from free stream to the nose of the fuselage of an aircraft is
measured in a wind tunnel @ 200C to be 34 kPa with a wind tunnel s

AE 160 / ME 111 Dr. Nikos J. Mourtos Flow Similarity
Define
The drag characteristics of a torpedo will be studied in a water tunnel using a 1:5
scale model. The tunnel operates with freshwater at 200C, wherea

Dr. Nikos J. Mourtos AE 160
Workout Problem
Given:
Total mass flow rate of air entering the engine
300 kg/s
Speed of air entering the engine
300 m/s
Engine bypass ratio
2.5
Fan exit speed
600 m/s
Core exit speed
1,000 m/s
Find: Thrust of the engine.

Dr. Nikos J. Mourtos AE 160 / ME 111
MOMENTUM (Newtons 2nd Law of Motion)
Case 1 Propeller
Consider the free-body diagram of an airplane in level flight at constant speed.
Figure 1 Free body diagram for an airplane in level flight with constant speed.
The

Dr. Nikos J. Mourtos AE 160
Calculation of drag from wake profile
Define
Determine the drag force per meter length of the cylinder shown.
Explore
This is a classic momentum equation problem.
Draw a CV around the cylinder, apply the momentum equat

Dr. Nikos J. Mourtos AE 160
Drag calculation from wake traverse measurements
Define
A 2-D body with a characteristic length of 25 cm was tested for drag in a 50 m/s
standard, sea level, free air stream. The following velocity distribution was mea

Dr. Nikos J. Mourtos AE 160 Workout
Lift and drag calculation from wall pressure distributions and wake profiles in a
wind tunnel
Define
An airfoil is mounted in a 2-D wind tunnel as shown above. The wind tunnel length,
height, and width