The Mach number is used to evaluate whether the incompressibility can be assumed or the flow must be solved as compressible.

In general, this is the case where the Mach number in part or all of the flow exceeds 0. 3.

The Mach. 3 value is rather arbitrary, but it is used because gas flows with a Mach number below that value demonstrate changes in density with respect to the change in pressure of less than 5 %.

It is defined as the range of speeds between the critical Mach number, when some parts of the airflow over an aircraft become supersonic, and a higher speed, typically near Mach 1. 2, when all of the airflow is supersonic.

Thus, when the fluid finally does strike the object, it is forced to change its properties -- temperature, density, pressure, and Mach number -- in an extremely violent and irreversible fashion called a shock wave.

Here is a critique due to Mach arguing that only relative motion is established:

The fastest speed flown during an air show is 700 mph ( just under Mach 1 ) and the slowest speed is 120 mph.

For flow of gases, to determine whether to use compressible or incompressible fluid dynamics, the Mach number of the flow is to be evaluated.

* is the lift coefficient at the desired angle of attack, Mach number, and Reynolds number

The BrahMos cruise missile which is a joint venture between India and Russia, is the fastest cruise missile in the world with a top speed of Mach 2. 8-3.

By 2000, most large-scale ( Mach-like ) efforts had ended, although OpenStep used an adapted Mach kernel called XNU, which is now used in the OS known as Darwin, which is the open source part of Mac OS X .. As of 2012, the Mach-based GNU Hurd is also functional and its inclusion in testing versions of Arch Linux and Debian in progress.

* GNU Mach, the microkernel upon which GNU Hurd is based

In fluid mechanics, Mach number ( or ) ( generally, sometimes or ) is a dimensionless quantity representing the speed of an object moving through air or other fluid divided by the local speed of sound.

: is the Mach number,

GNU Hurd consists of a set of protocols and server processes ( or daemons, in Unix terminology ) that run on the GNU Mach microkernel ; together they are intended to form the kernel of the GNU operating system.

* Mach ( kernel ), an operating systems kernel technology

Mach was developed as a replacement for the kernel in the BSD version of UNIX, so no new operating system would have to be designed around it.

Today further experimental research on Mach appears to have ended, although Mach and its derivatives are in use in a number of commercial operating systems, such as NeXTSTEP and OPENSTEP, and most notably Mac OS X using the XNU operating system kernel which incorporates an earlier ( non-microkernel ) Mach as a major component.

Additionally, Mach allowed any program to handle privileges that would normally be given to the operating system only, in order to allow user space programs to handle things like interacting with hardware.

Under Mach, and like UNIX, the operating system again becomes primarily a collection of utilities.

While this same approach worked for Mach's ports as well, under Mach the operating system was assumed to be much more fluid, with ports appearing and disappearing all the time.

Mach 3 led to a number of efforts to port other operating systems parts for the microkernel, including IBM's Workplace OS and several efforts by Apple Computer to build a cross-platform version of the Mac OS.

Under Mach, the bits of the operating system are isolated in servers, which are able to run, like any other program, on any processor.

When Mach was first being seriously used in the 2. x versions, performance was slower than traditional monolithic operating systems, perhaps as much as 25 %.

When Mach 3 attempted to move most of the operating system into user-space, the overhead became higher still: benchmarks between Mach and Ultrix on a MIPS R3000 showed a performance hit as great as 67 % on some workloads.

Under Mach this wasn't possible because the kernel had no real idea what the operating system consisted of.

Likewise Mach caused problems when memory had been moved by the operating system, another task that only really makes sense if the system has more than one address space.

A team led by Avie Tevanian, who had joined the company after working as one of the Mach kernel engineers at Carnegie Mellon University, was to develop the NeXTSTEP operating system.

* SPIN ( operating system ), an OS based on Mach

* No known air breathing engine is capable of operating at orbital speed within the atmosphere ( for example hydrogen fueled scramjets seem to have a top speed of about Mach 17 ).

The fact that OSF / 1 was one of the first operating systems to use the Mach kernel is cited as support of this assertion.

The Mach virtual memory management system was also adopted by the BSD developers at CSRG, and appears in modern BSD-derived UNIX systems, such as FreeBSD.

Mach developed on Accent's IPC concepts, but made the system much more UNIX-like in nature, even able to run UNIX programs with little or no modification.

While this is common in modern systems, Mach was the first system to define tasks and threads in this way.

Under Mach, the IPC system was used for this role instead.

This allowed the system to be distributed over multiple processors, either using shared memory directly as in most Mach messages, or by adding code to copy the message to another processor if needed.

Under Mach this was well defined and easy to implement ; it was the very process of accessing that memory, the ports, that was made a first-class citizen of the system.

A key goal of Mach is to be a distributed system capable of functioning on heterogeneous hardware.

Mach was initially hosted as additional code written directly into the existing 4. 2BSD kernel, allowing the team to work on the system long before it was complete.

As portions were completed various parts of the BSD system were re-written to call into Mach, and a change to 4. 3BSD was also made during this process.

These early Mach versions included the majority of 4. 3BSD in the kernel, a system known as POE Server, resulting in a kernel that was actually larger than the UNIX it was based on.

Unwieldy UNIX licensing issues were also plaguing researchers, so this early effort to provide a non-licensed UNIX-like system environment continued to find use, well into the further development of Mach.

If the existing system could be ported to run on Mach, it would seem it would then be easy to change the platform underneath.

Mach 2. 5 was also selected for the NeXTSTEP system and a number of commercial multiprocessor vendors.

For instance, Mach used a permissioning and security system patterned on UNIX's file system.