b) A horizontal needle contains a solution to be injected intravenously. The cro

Question

b) A horizontal needle contains a solution to be injected intravenously. The cross-sectional area of the main reservoir is about 2.31 ? 10?5 m2. When no forces are applied to the back of the needle to eject the solution, there is 1 atmosphere of pressure in the main reservoir of the solution. Suppose that F = 2.19 N of force is applied to the back of the needle, causing the ejection of the solution. How quickly does the liquid exit the needle? Assume the pressure inside the needle stays at 1 atm and that the speed of the fluid in the main reservoir is much much slower (negligibly so) than the speed of the fluid upon exiting. m/s

Explanation / Answer

(A) in vertical,

yf - yi = v0y t + a t^2 / 2

0 - 1 = 0 - 9.8 t^2 /2

t = 0.452 sec  

and d = v t

v = 0.60 /0.452 = 1.33 m/s

Applying Bernoulli's equation,

P1 + rho g h1 + rho v1^2 /2 = P2 + rho g h2 +rho v2^2 / 2

P_atm + (1000 x 9.8 x h) + 0 = P_atm + 0 + (1000 x 1.33^2 / 2)

h = 0.09 m Or 9 cm  

(B) delta(P) = rho v^2 / 2

F / A = rho v^2 / 2

(2.19) / (2.31 x 10^-5) = 1000 v^2 / 2

v = 13.8 m/s

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