(Solved): A hypodermic syringe contains water. The barrel of the syringe has a cross-sectional area of A= 10^- ...

A hypodermic syringe contains water. The barrel of the syringe has a cross-sectional area of A= 10^-5 m^2, and the needle has a cross-sectional area of a = 10^-8 m^2. In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force of magnitude F= 3.00 N is exerted on the plunger, making water squirt horizontally from the needle. What is the speed of the water v2 as it leaves the needle’s tip?

Hint:
1. Use Continuity Equation and assume that water is an incompressible fluid.
2. Apply Bernoulli’s Equation
3. If v2 = 1000v1, then you can approximate v1^2? 0.???????

A hypodermic syringe contains water. The barrel of the syringe has a cross-sectional area of \( A=10^{-5} \mathrm{~m}^{2} \), and the needle has a cross-sectional area of \( a=10^{-8} \mathrm{~m}^{2} \). In the absence of a force on the plunger, the pressure throughout is \( 1 \mathrm{~atm} \). A force of magnitude \( F=3.00 \mathrm{~N} \) acts on the plunger, making water squirt horizontally from the needle. What is the speed of the water \( v_{2} \) as it leaves the needle's tip? (25 pts) Hint: 1. Use Continuity Equation and assume that water is an incompressible fluid. 2. Apply Bernoulli's Equation 3. If \( v_{2}=1000 v_{1} \), then you can approximate \( v_{1}^{2} \approx 0 \).