Find the force exerted on your eardrum due to the water above when you are swimm

Question

Find the force exerted on your eardrum due to the water above when you are swimming at the bottom of a pool that is 5.5 m deep. First, find the unbalanced pressure on the eardrum: then, calculate the force exerted on it. The estimated area of an eardrum is 1 times 10^-4 m^2 B. Along a highway rain water is pumped through an straight horizontal underground pipe. The water enters at a speed of 3 m/s through a diameter opening of 0.16m and exits under a pressure of 0.05 atm through a diameter opening of 0.24 m, find a) the flow rate and b) the pressure at the 0.16 m diameter end. 1 atm = 1 times 10^5 N/m^2

Explanation / Answer

7A.

P = Po + rho g h

deltaP = P - P0 = rho g h

= 1000 x 9.8 x 5.5

= 53900 Pa

F = deltaP A

= (53900) (1 x 10^-4)

= 5.39 N

7B.

(A) flow rate = A v = 3 x (pi x (0.16/2)^2)

= 0.0603 m^3 / s

(b) 0.0603 = v pi (0.24/2)^2

v = 1.33 m/s

P + rho v^2 /2 = constant

P + (1000 x 3^2 / 2) = (0.05 x 101325) + (1000 x 1.33^2 / 2)

P = 1384.5 Pa Or 13.8 x 10^-3 atm

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