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

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To calculate the pressure difference needed to inject water at a rate of 1.5 g/s through a hypodermic needle, the relevant equation is V = [(P1-P2)(pi*r^4)]/(8*n*L). The needle dimensions are 3.2 cm in length and 0.25 mm in diameter, with the radius converted to 0.000125 m. The viscosity of water at 20°C is approximately 0.0010055 Pa·s. To find the required velocity for the flow rate, the conversion from mass flow rate to volumetric flow rate is necessary, using the relationship between volume flow and velocity. Understanding these calculations will lead to determining the pressure difference needed for the injection.
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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?
 
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Pressure energy is converted into kinetic energy.
To convert volume flow into velocity, you can consider:

\dot{V}= A\cdot v
 

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