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