Makefile made by qmake only works on my pc - qt

Question

For a university project we made an OpenGL application which uses Qt for the GUI. When I use qmake -spec macx-g++ project.pro I can make a Makefile, and if I then do make it correctly makes the application. However, when I then send the complete folder to the other person in the project and he does make he gets the error
Makefile:209: warning: overriding commands for target `moc_window.cpp'
Makefile:203: warning: ignoring old commands for target `moc_window.cpp'
make: *** No rule to make target `/usr/lib64/qt-3.3/mkspecs/default/qmake.conf', needed by `Makefile'. Stop.
However, when in the same folder he does qmake; make it does work correctly. The problem is that when handing the code in we don't know if the professor has qmake available, so we would like it to work by only using make. Are we missing something that should be addded to have the Makefile made with qmake work, without having to do qmake again? Our .pro file is below.
TEMPLATE = app
TARGET = smoke
QT = core gui opengl
greaterThan(QT_MAJOR_VERSION, 4): QT += widgets
SOURCES += \
fluids.cpp \
simulation.cpp \
visualization.cpp \
window.cpp \
myglwidget.cpp \
vector.cpp \
grid.cpp \
scalar.cpp
HEADERS += \
window.h \
myglwidget.h \
simulation.h \
vector.h \
grid.h \
visualization.h \
scalar.h
INCLUDEPATH += fftw-2.1.5/include /usr/local/include include
LIBS += -L"$$_PRO_FILE_PWD_/fftw-2.1.5/lib" -lrfftw -lfftw -framework OpenGL -framework GLUT -stdlib=libc++
QMAKE_CXXFLAGS += -stdlib=libc++
QMAKE_CXXFLAGS += -std=c++11
FORMS += \
window.ui

Answer 1

The build directory is not portable. It is only ever meant to work on the system where you executed qmake, and for the particular Qt install that you ran qmake from. Recall that each Qt install has its own qmake, so e.g. if you have three Qt versions, each provides its own qmake that you must use to build a project using that version.
The project you ship should contain the .pro file, the sources, and whatever else the build calls for, like icon files, resources, etc.
The recipient, to build it, should:
Create a build folder.
cd into the build folder.
qmake /path/to/sources/project.pro && make -j
That's how you distribute and build Qt projects.
why does qmake not build the application directly?
Why do you not make your own shoes? The reasons are the same. Don't reinvent the wheel.
Of course, engineers sometimes have an itch to scratch. Enter Qt Build System (qbs). If your project's build is given as a .qbs file, then you do:
Create a build root folder.
cd into the build root folder.
qbs -f /path/to/sources/project.qbs - this builds the project.