2.1 KiB
Homework 6 - Aidan Sharpe
1
A hose lying on the ground has water coming out of it at a speed of 5.4 meters/sec. You lift the nozzle of the hose to a height of 1.3 meters above the ground. At what speed does the water now come out of the hose? (Note: Atmospheric pressure acts on the fluid at both points). List any assumptions.
v_1 = 5.4 \text{[m/s]}h_1 = 0 \text{[m]}h_2 = 1.3 \text{[m]}{1\over2}\rho v_1^2 + \rho g h_1 = {1\over2} \rho v_2^2 + \rho g h_2{1\over2}(5.4^2) + 9.81 (0) = {1\over 2} v_2^2 + 9.81 (1.3)Solve for v_2 algebraically:
v_2 = 1.911 \text{[m/s]}2
A dam is holding back the water in a lake. There is a small hole 1.4 meters below the surface of the lake. At what speed does water exit the hole? List any assumptions. (Note: if the hole is small, what is a safe assumption for the particles at the top of the lake)
P = \rho g h\rho = 1000 \left[{\text{kg} \over \text{m}^3}\right]h = 1.4 \text{[m]}P = 9.81(1000)(1.4) = 13720 \text{[Pa]}P_1 + {1\over2}\rho v_1^2 + \rho g h_1 = P_2 + {1\over2}\rho v_2^2 + \rho g h_2{1\over2}\rho v_2^2 = P_1v_2 = 5.23 \text{[m/s]}3
A basketball is floating in a bathtub full of water. The basketball has a mass of 0.5 kg and a diameter of 22 cm.
a)
What is the buoyancy force? Draw a Free Body Diagram and apply equations.
F_b = mg = 4.9 \text{[N]}b)
What is the volume of water displaced by the ball? (consider it a sphere and use Archimedes principle)
F_b = \rho v gv = {4.9 \over \rho g} = 5 \times 10^{-4} \text{[m}^3]c)
What is the average density of the basketball?
d = {0.5 \over {4\over3}\pi r^3} = {0.5 \over {4\over3}\pi {0.11}^3} = 89.68 \left[{\text{kg} \over \text{m}^3}\right]4
You need to extend a 2 cm diameter pipe, but you have only a 1.10 cm diameter pipe on hand. You make a fitting to connect these pipes end to end. If the water is flowing at 2.50 cm/sec in the wide pipe, how fast will it be flowing through the narrow one?
v_1 A_1 = v_2 A_20.025 (\pi 0.02^2) = v_2 (\pi 0.0055^2)v_2 = 0.083 \text{[m/s]} = 8.3 \text{[cm/s]}