A hypodermic syringe has a plunger area 2.5 cm^2 and a 5.0 X10^-3 needle. (a) If

Question

A hypodermic syringe has a plunger area 2.5 cm^2 and a 5.0 X10^-3 needle. (a) If a 1.0-N force is appliedto the plunger, what is thegauge pressure in the syringe's chamber? (b) If a small obstruction is at the end of the needle, whatforce does the fluid exert on it? (c) If the blood pressure in a vein is 50 mm Hg, what forcemust be applied on the plunger so that fluid can be injected intothe vein? A hypodermic syringe has a plunger area 2.5 cm^2 and a 5.0 X10^-3 needle. (a) If a 1.0-N force is appliedto the plunger, what is thegauge pressure in the syringe's chamber? (b) If a small obstruction is at the end of the needle, whatforce does the fluid exert on it? (c) If the blood pressure in a vein is 50 mm Hg, what forcemust be applied on the plunger so that fluid can be injected intothe vein?

Explanation / Answer

given that area of plunger = A pl = 2.5cm2 = 2.5* 10-4 m2 area of needle = A N = 5 * 10-3cm2 = 5 * 10-7 m2 a) applied force to plunger Fp = 1.00N pressure on the syringe = ps =Fp/Ap                                            = 1.00N/2.5 * 10-4 m2                                                            = 0.04 * 105 N/m2 now guage pressure = pg = ps-pa                                         = 0.04 * 105 N/m2 - ( 1.01 * 105N/m2) = -0.97* 105 N/m2 b) force exert on needle due to obstruction =Ps * AN          plug invalues                                  = 0.2 * 10-2N c) given blood pressure in a vein =pb = 50mmHg                                                               = 50 * 1.01 * 105 N/m2 /760                                                                                      = 0.066447 * 105 N/m2      the force to be applied on the plunger toinjected in to vein Fpv = pbAp        plug in values  Fpv = 1.66118N

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