If we have water that flows from a large tank into a pipe with a D = 3 in, and t

Question

If we have water that flows from a large tank into a pipe with a D = 3 in, and then into the atmosphere as shown in the figure. If h = 20 ft, and we know that viscous effects are neglected:

1) What is the velocity at the exit to the pipe?

2) What is the volumetric flow rate at the exit of the pipe?

3) What is the mass flow rate at the exit to the pipe?

4) What is the mass flow rate at the entrance to the pipe?

NOTE:
**Please explain step by step and write the formulas used**
Clear and solved by hand problems will have greater preference.

Explanation / Answer

1. V^2 = 2gh   

V = velocity , g = accleration due to gravity = 9.8 m/sec^2

h = 20ft = 0.3048 m

V = 2 x 9.8 x 20 x0.3048 = 119.4 m/ sec

2. voumetric flow rate (Q)= VxA

v= velocity , A = area

Q = 119.4x3.14x0.0762^2 = 2.177 m^3 /sec

3. mass flow rate at the exit = volume flow rate x density = 2.177 x 1000 = 2177 kg /sec (density of water = 1000kg/m3)

4. mass flow rates at the exit is equal to entrance.

mass flow rate at the entrance to the pipe = 2.177 kg/sec

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