A D0 = 8-m-diameter tank is initially filled with water 2 m above the center of aD = 10-cm-diameter valve near the bottom. The tank surface is open to the atmosphere, and the tank drains through aL = 80-m-long pipe connected to the valve. The friction factor of the pipe is given to be f= 0.015, and the discharge velocity is expressed as

where z is the water height above the center

of the valve. Determine (a) the initial discharge velocity from the tank and (b) the time required to empty the tank. The tank can be considered to be empty when the water level drops to the center of the valve.

Part (a)

Step 1 of 9:

To determine the initial discharge velocity from the tank which is at atmospheric pressure.

The diameter of the tank D0 = 8.00 m

Height of the water in tank z = 2.00 m

Diameter of the valve/pipe D = 10.0 cm or 0.10 m

The length of the pipe connected to the valve L = 80.0 m

Frictional factor of the pipe f = 0.015

Acceleration due to gravity g = 9.81 m/s2

Step 2 of 9:

The discharge velocity is expressed as

= ------(1)

Inserting the known numerical values

=

= m/s

= 1.7049 m/s or 1.705 m/s

The initial discharge velocity from the tank is 1.705 m/s

Part (b)

Step 3 of 9:

To determine the time required to empty the tank

Now consider the height of the tank is z.

The diameter of the tank D0 = 8.00 m

Radius of the tank =

Height of the water in tank z = 2.00 m

Diameter of the valve/pipe D = 10.0 cm or 0.10 m

Radius of the tank =

The length of the pipe connected to the valve L = 80.0 m

Frictional factor of the pipe f = 0.015

Acceleration due to gravity g = 9.81 m/s2

Step 4 of 9:

The volumetric flow rate is expressed as

= = ----(2)

Where is change in volume of the tank ,is discharge velocity and is the area of cross section the pipe.

Rearranging the equation (2)

= ----(3)

Step 5 of 9:

Change in volume is expressed as

=

Where is the area of the tank and the negative sign indicates that the volume of the tank is decreasing with respect to time. z reduces to 0 from z.

= ------(4)