A large tank, 25 m in height and open at the top, is completely filled with salt
ID: 1705163 • Letter: A
Question
A large tank, 25 m in height and open at the top, is completely filled with saltwater (density 1025 kg/m^3). A small drain plug with a cross-sectional area of 4.0 x 10^-5 m^2 is located 5.0 m from the bottom of the tank. The plug breaks loose from the tank, and water flows from the drain.(a) Calculate the force exerted by the water on the plug before the plug breaks free.
(b) calculate the speed of the water as it leaves the hole in the side of the tank
(c) Calculate the volume flow rate of the water from the hole
Thank you so much!!
Explanation / Answer
A large tank open at the top at a height is h = 25.0m
tank is filled with salt water, density of salt water is = 1025 kg / m^3
A small drain plug with a crosssectional area is A = 4.0 *10^-5 m^2
located at a height h_0 = 5.0m
H = h - h_0
= 25.0 - 5.0
= 20.0m
(a ) force exerted by the water on the plug before the plug breaks free is
F = P A
= g H * A
= 1025 kg / m^3 * 9.8 m/s^2 * 20.0m * 4.0 *10^-5 m^2
= 8.036N
(b ) From Bernoullis Equation
speed of the water as it leaves the hole in the side of the tank is
(v_in)^2/ 2 + P_in/ = (v_out)^2/ 2 + P_out /
0+ g H / = (v_out)^2/ 2 +0
v_out = 2 g H /
= 2 * 9.8 * 20.0m
= 19.7 m/s
c ) the volume flow rate of the water from the hole
from equation of contunity
v_out* A = V
19.7 m/s * 4.0 *10^-5 m^2
= 7.88*10^-4 m^3 /s
= 0.788 L / s
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