ME 363 - Fluid Mechanics
Homework #6
Due October 17, 2007
Fall Semester 2007
1] This problem involves a shock tube: a length of pipe that contains air and is closed (sealed) at both ends. Some
details of the shock tube and its operation are at http://silver.neep.wisc.edu/~shock/shocktube.html but are not
needed to solve the problem. All you must know is that for one portion of a test, the air in the tube behaves as
follows: in each millisecond, 0.085 kg of air is accelerated from rest to a velocity of 764 m/s. Find the force that
the shock tube hardware must withstand to accommodate the acceleration of the air inside the shock tube.
{Note: don’t be satisfied by just getting the right answer. It is important to understand the problem solution
process.}
2] Gravel is dumped from a hopper, at a rate of 650 N/s, onto a moving belt. The gravel then passes off the end of
the belt. The drive wheels are 80 cm in diameter and rotate clockwise at 150 rev/minute. Neglect system
friction. a) Find the power required to drive this belt. b) Find the power required to drive the belt after the
hopper supply has stopped abruptly so that the situation appears as shown.
3] The cart moves at a constant velocity V0 = 12 m/s and collects water with a scoop 80 cm wide that dips h=2.5
cm into a pond. Neglect air drag and wheel friction. Find the force required to keep the cart moving using a) a
control volume that contains the cart and scoop and moves with the cart and b) a large, stationary control
volume that contains the moving cart as well as the entire pond. {for this case, if you like, imagine that the cart
is being pulled by a string extending outside of your CV.}
4] A modern turbofan engine in a commercial jet takes in air, part of which passes through the compressors,
combustion chamber, and turbine, and the rest of which bypasses the compressor and is accelerated by the fans.
The mass flow rate of the bypass air to the mass flow rate through the compressor-combustion-turbine path is
called the ‘bypass ratio.’ The total flow rate of air entering a turbofan is 300 kg/s with a velocity of 300 m/s.
The engine has a bypass ratio of 2.5. The bypass air exits at 600 m/s, whereas the air through the compressorcombustor-turbine path exits at 1000 m/s. What is the thrust of the turbofan engine?
5] An engineer is measuring the lift and drag on an airfoil section mounted in a two-dimensional wind tunnel. The
wind tunnel is 0.5 m high and 0.5 m deep (into the page). The upstream wind velocity is uniform at 10 m/s, and
the downstream velocities are 12 m/s and 8 m/s as shown. The vertical component of velocity is zero at both
stations. The test section is 1 m long. The engineer measures the pressure distribution in the tunnel along the
upper and lower walls and finds
Pu = 100 – 10x – 20x(1-x) [Pa, gage]
Pl = 100 – 10x + 20x(1-x) [Pa, gage]
where x is the distant in meters measured from the beginning of the test section. The gas density is
homogeneous throughout and equal to 1.2 kg/m3. Find the lift and drag forces acting on the airfoil section.
Problem #1
Problem #2a
Problem #2b
Problem #3
Problem #4
Problem #5
Solution #1
Solution #2a
Solution #2b:
Solution #3a
Solution #3b:
4] A modern turbofan engine in a commercial jet takes in air, part of which passes through the compressors,
combustion chamber, and turbine, and the rest of which bypasses the compressor and is accelerated by the fans.
The mass flow rate of the bypass air to the mass flow rate through the
compressor-combustion-turbine path is called the ‘bypass ratio.’ The
total flow rate of air entering a turbofan is 300 kg/s with a velocity of
300 m/s. The engine has a bypass ratio of 2.5. The bypass air exits at
600 m/s, whereas the air through the compressor-combustor-turbine path
exits at 1000 m/s. What is the thrust of the turbofan engine?
5] An engineer is measuring the lift and drag on an airfoil section mounted in a two-dimensional wind tunnel. The
wind tunnel is 0.5 m high and 0.5 m deep (into the page). The upstream wind velocity is uniform at 10 m/s, and
the downstream velocities are 12 m/s and 8 m/s as shown. The vertical component of velocity is zero at both
stations. The test section is 1 m long. The engineer measures the pressure distribution in the tunnel along the
upper and lower walls and finds
Pu = 100 – 10x – 20x(1-x) [Pa, gage]
Pl = 100 – 10x + 20x(1-x) [Pa, gage]
where x is the distant in meters measured from the beginning of the test
section. The gas density is homogeneous throughout and equal to 1.2
kg/m3. Find the lift and drag forces acting on the airfoil section.