Math Problem Statement

A hypodermic syringe contains a medicine with the density of water (figure below). The barrel of the syringe has a cross-sectional area of 2.38 ✕ 10−5 m2. In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force F of magnitude 2.28 N is exerted on the plunger, making medicine squirt from the needle. Determine the medicine's flow speed through the needle. Assume the pressure in the needle remains equal to 1.00 atm and that the syringe is horizontal. A syringe is aligned horizontally, with the plunger on the left side, the needle on the right side, and the barrel between them in the middle. The cross-sectional area of the barrel is labeled A1, and the cross-sectional area of the needle is labeled A2. An arrow labeled vector F is outside and to the left of the syringe, and points to the right toward the plunger. An arrow labeled vector v2 is outside and to the right of the syringe, and points to the right away from the needle. The fluid in the barrel of the syringe is labeled P1, and the fluid in the needle is labeled P2.

Solution

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Math Problem Analysis

Mathematical Concepts

Fluid Mechanics
Bernoulli's Equation
Continuity Equation

Formulas

Bernoulli's equation
Continuity equation

Theorems

Principle of conservation of energy (Bernoulli's theorem)

Suitable Grade Level

College