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How to Determine the Water Level of a Truncated Cone Tank? One of the points is usually chosen at the location where an unknown variable is to be found. The second point is usually chosen at a location where some information is available or is open to the atmosphere since the absolute pressure there is known to be the atmospheric pressure (P_atm). Considering this recommendation, if we are supposed to find the outlet velocity in the large reservoir shown in Fig. 2, the best two points to select are at water level (P = P_atm and v is almost 0) and at the outlet (P = P_atm and the unknown parameter v_z). From Bernoulli's law, we have the exit velocity from the tank to be: v = âˆš(2g(h-y)) (2) Truncated cone tank: R_t -- 35 cm R_b h(t) h(0) Uniform circular tank Fluid level K v P, Elevation, y Head, Reference plane v_P2 y_2 Figure 4. Cross section of a truncated cone tank Equation 4 can be used to find x: R_bR = 35 + x (4) By writing equation 2 as a function of time and putting the total volume of water leaving the tank equal to the total water supplied (Fig. 3), the water level equation can be found. Similarly, R can be found as a function of h(t) using equation 5: R_bR = x + x + y ah(r) at (3) (5) Now, the water level equation can be found by putting the total volume of water leaving the tank equal to the total water supplied. Solving equation 3 gives the instantaneous water level h(t) in the water tank at any time t. D h(t) H_O Velocity, v(t) Figure 3. Water coming out of the tank through a valve (for finding the water level equation)

Name: how to determine the water level of a truncated cone tank one of the points is usually chosen at the location where an unknown variable is to be found the second point is usually chosen at a 45976
Uploaded: 2024-03-31T04:44:25-08:00
Duration: 3 min 26 s
Channel: Numerade
Description: how to determine the water level of a truncated cone tank one of the points is usually chosen at the location where an unknown variable is to be found the second point is usually chosen at a 45976

          How to Determine the Water Level of a Truncated Cone Tank?

One of the points is usually chosen at the location where an unknown variable is to be found. The second point is usually chosen at a location where some information is available or is open to the atmosphere since the absolute pressure there is known to be the atmospheric pressure (P_atm). Considering this recommendation, if we are supposed to find the outlet velocity in the large reservoir shown in Fig. 2, the best two points to select are at water level (P = P_atm and v is almost 0) and at the outlet (P = P_atm and the unknown parameter v_z). From Bernoulli's law, we have the exit velocity from the tank to be:

v = âˆš(2g(h-y))

(2)

Truncated cone tank:
R_t
--
35 cm
R_b

h(t)
h(0)

Uniform circular tank
Fluid level
K
v
P, Elevation, y
Head, Reference plane
v_P2
y_2

Figure 4. Cross section of a truncated cone tank

Equation 4 can be used to find x:

R_bR = 35 + x

(4)

By writing equation 2 as a function of time and putting the total volume of water leaving the tank equal to the total water supplied (Fig. 3), the water level equation can be found. Similarly, R can be found as a function of h(t) using equation 5:

R_bR = x + x + y

ah(r) at

(3)

(5)

Now, the water level equation can be found by putting the total volume of water leaving the tank equal to the total water supplied. Solving equation 3 gives the instantaneous water level h(t) in the water tank at any time t.

D
h(t)
H_O
Velocity, v(t)

Figure 3. Water coming out of the tank through a valve (for finding the water level equation)

how to determine the water level of a truncated cone tank one of the points is usually chosen at the location where an unknown variable is to be found the second point is usually chosen at a 45976

Added by Josep M.

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