# Can force be expressed as mass flow rate times velocity

I know that F=ma which give the units of kg.m/s/s (in SI units) but can force also be expressed as mass flow rate times velocity which also has the same units? Example: water coming out a hose or gas coming out a spray can?

## Answers and Replies

Gold Member
I know that F=ma which give the units of kg.m/s/s (in SI units) but can force also be expressed as mass flow rate times velocity which also has the same units? Example: water coming out a hose or gas coming out a spray can?

Newton's law is actually that force is the rate of change of momentum with time,
$$F = \dfrac{d(mv)}{dt}.$$
Therefore,
$$F = m\dfrac{dv}{dt} + v\dfrac{dm}{dt}.$$
So, if you have a constant velocity, then yes, force can be simply the rate of change of mass times velocity.

EastWindBreaks
Thanks. So for water flowing through a pipe (kg/s) at constant velocity, what does the force calculated by m(dot).v represent? is it the frictional force on the pipe?

Nidum
Gold Member
Mass flow is simply Kg/sec . Actual velocity depends on density and pipe size .

No dynamic force is generated until something happens to accelerate or de-accelerate the flow .

This can be a change in cross sectional area of pipe or a change of flow direction as in a turbine .

Usually better to think of pressures rather than forces when dealing with fluids .

Cool, thanks

Gold Member
Thanks. So for water flowing through a pipe (kg/s) at constant velocity, what does the force calculated by m(dot).v represent? is it the frictional force on the pipe?

It would be the force experienced by, say a plate that goes sprayed by that water stream if all of the water from that stream was then deflected sideways when it hits the plate, for example.

It would be the force experienced by, say a plate that goes sprayed by that water stream if all of the water from that stream was then deflected sideways when it hits the plate, for example.
Thanks, a real life example makes it easier to visualize
I wounder if F=m(dot).v could be applied to a spray can that is spraying gas at the rate of m(dot) and gas velocity v, would the nozzle experience a force, (disregarding the air pressure and friction) ?