How Much Pressure Is Needed to Inject Water at 1.5g/s Through a Tiny Needle?

[SoccaCrazy24]

A patient is given an injection with a hypodermic needle 3.2 cm long and 0.25 mm in diameter. Assuming the solution being injected has the same density and viscosity as water at 20°C, find the pressure difference needed to inject the solution at the rate of 1.5 g/s.

ok I have the equation V = [(P1-P2)(pi*r^4)]/(8*n*L)
(P1-P2)= pressure difference
r= .000125 m
n= .0010055
L= .032 m
I do not know how I am suppose to transform 1.5g/s to m/s because I am unsure of how to transfer grams to meters... once i get that I can find the difference in pressure...

In a similar problem with diameter being .28mm the answer came out to be 320kPa... help?

 

[mezarashi]

Pressure energy is converted into kinetic energy.
To convert volume flow into velocity, you can consider:

$$\dot{V}= A\cdot v$$