A 20 mL syringe has an inner diameter of 4.0 mm, a needle inner diameter of 0.58 mm, and a plunger pad diameter (where you place your finger) of 1.2 cm. A nurse uses the syringe to inject medicine into a patient's vein and so has to push against the patient's blood pressure which is 140 over 96.0.
Assuming that the medicine has the same density as water ($1000 kg/m^3$) and that the syringe is being held horizontal, what is the pressure value inside of the syringe?
Since pressure values are so large when using Pascal, please be safe and enter all of the digits in your answer up to the ones place.