Water moves through a constricted pipe in steady, idea flow. At the lower point

Question

Water moves through a constricted pipe in steady, idea flow. At the lower point shown in the figure below, the pressure is 1.75 times 10^5 Pa and the pipe radius is 3.00 an. At the higher point located at y = 2.50m, the pressure is 1.20 times 10^5 Pa and the pipe radius is 1.50 cm. Find the speed of flow in the lower section. Find the speed of flow n the upper section. Find the volume flow rate through the pipe 20.0:L tank of carbon dioxide gas (CO_2) is at a pressure of 9.50 times 10^5 pa and temperature of 19.0 degree C. Calculate the temperature of the gas in Kelvin. Use the ideal gas law to calculate the number of moles of gas in the tank.

Explanation / Answer

Bernouilli's Principle:
(1/2) (vL)^2 + (pL)/rho + g(zL) = (1/2) (vU)^2 + (pU)/rho + g(zU)
(1.75 - 1.20)*10^5 Pa/(1000 kg/m^3) = (9.8 m/s^2)(2.50 m) + (1/2)[(vU)^2 - (vL)^2]
(vU)^2 - (vL)^2 = 2 (55 m^2/s^2 - 24.5 m^2/s^2) = 61 m^2/s^2

Also, (vL)/(vU) = (15/30)^2 = 0.25 [continuity equation]

B)
(vU)^2 - (0.25 vU)^2 = 61 m^2/s^2
vU = sqrt(61/0.0625) m/s = 31.24 m/s

A)
vL = 0.25 vU =0.25*31.24= 7.81m/s

c)
Flow rate = (31.24 m/s)(pi)(0.015 m)^2
= 0.022 m^3/s (22 liters per second)

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