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You may have learned Newton's 2nd law of motion, "force is equal to the rate of change of momentum". In fluids, the rate of change of mass, dm/dt, often abbreviated \dot{m}, is important. Use the product rule to find the form of Newton 2 that includes the possibility of mass flow.
If the flow is "steady", i.e. the mass flow in to a certain volume equals the mass flow out, the formula you derived simplifies to F = \dot{m}v.
When we resolve this formula in any particular direction, we call it the "steady flow momentum equation".
A tank (pictured) has a chemical (density 800kg/m^3) flow of 1kg/s going through from left to right. The inlet pipe has an area 100cm^2, and the outlet pipe has an area 50cm^2. If the inlet pressure is 1MPa, what is the output pressure? Hint: mass is conserved, and the mass flow in a pipe of area A with fluid velocity V is just \dot{m} = \rho AV.
Can you see any structural problems that might arise with this tank?
Would it make a significant difference if the tank were aligned vertically or horizontally?
Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.
A look at the fluid mechanics questions that are raised by the Stonehenge 'bluestones'.