In large buildings, hot water in a water tank is circulated through a loop so that the user doesn’t have to wait for all the water in long piping to drain before hot water starts coming out. a certain recirculating loop involves 40-m-long, 1.2-cm-diameter cast iron pipes with six 90° threaded smooth bends and two fully open gate valves. if the average flow velocity through the loop is 2 m/s, determine the required power input for the recirculating pump. take the average water temperature to be 60°c and the efficiency of the pump to be 76 percent. the density and dynamic viscosity of water at 60°c are rho = 983.3 kg/m3, μ = 0.467 × 10–3 kg/m·s. the roughness of cast iron pipes is 0.00026 m. the loss coefficient is kl = 0.9 for a threaded 90° smooth bend and kl = 0.2 for a fully open gate valve. (round the final answer to three decimal paces.)

The power input is 0.102 kW

Solution:

As per the question:

Length of the loop, L = 40 m

Diameter of the loop, d = 1.2 cm

Velocity, v = 2 m/s

Loss coefficient of the threaded bends,

Loss coefficient of the valve,

Dynamic viscosity of water,

Density of water,

Roughness of the pipe of cast iron,

Efficiency of the pump,

Now,

We calculate the volume flow rate as:

where

= Volume rate flow

A = Area

v = velocity

For this, Reynold's N. is given by:

Since, > 4000, the flow is turbulent in nature.

Now,

With the help of the Colebrook eqn, we calculate the friction factor as:

f = 0.05075

Now,

To calculate the total head loss:

Now,

The drop in the pressure can be calculated as:

Now,

to calculate the input power:

another example of kinetic energy would be,

kinetic energy   >     moving energy

answer   >   letter choice (c),   a hammer falling off a table.

hope that !                                         : )

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