A palindrome is a number or a text phrase that reads the same backwards as forwards. For example, each of the following five-digit integers is a palindrome: 12321, 55555, 45554 and 11611. Write a C++ program that reads in a five-digit integer and determines whether it is a palindrome .

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Question

Water is pumped from a lower reservoir to a higher reservoir by a pump that provides 23 kW of useful mechanical power to the water. The free surface of the upper reservoir is 57 m higher than the surface of the lower reservoir. If the flow rate of water is measured to be 0.03 m³/s, determine the irreversible head loss of the system and the lost mechanical power during this process.

Solution

Step 1

Given;

Mechanical power by a pump, $P_m=23 kW$

Head difference between reservoirs, $H=57 m$

The flow rate of water, $Q=0.03 m^3/s$

Step 2

Now the mass flow rate of water, $\dot{m}=\rho .A.V=\rho .Q (Q=A.V)$

Here, A is the area of the pipe and V is the velocity of the flow. $\rho$ is the density of water=$1000 kg/m^3$

So, 

 $$\begin{gathered} \dot{m}=\rho .Q=1000\times 0.03 \\ m=30 kg/s \end{gathered}$$

Power required to deliver water into the higher reservoir, 

$$\begin{gathered} P=\dot{m}.g.H \\ P=30\times 9.81\times 57 \\ P=16775.1 W \\ P=16.775 kW \end{gathered}$$            ( g is the acceleration due to gravity=9.81 $m/s^2$ )

Now the lost mechanical power during this process;

 $$\begin{gathered} P_l=P_m-P \\ {P}_l=23-16.775 \\ {P}_l=\mathbf{6}\mathbf{.}\mathbf{225}\mathbf{ }\mathit{k}\mathit{W} \end{gathered}$$

and the irreversible head loss ($h_f$);

now, 

$$\begin{gathered} P_l=\dot{m}.g.h_f \\ 6.225\times {10}^3=30\times 9.81\times h_f \\ {h}_f=\mathbf{21}\mathbf{.}\mathbf{151}\mathbf{ }\mathit{m} \end{gathered}$$

Step 3

So the irreversible head loss, ${\mathit{h}}_{\mathbf{f}}\mathbf{=}\mathbf{21}\mathbf{.}\mathbf{151}\mathbf{ }\mathit{m}$ and the lost mechanical power during this process, $P_l=\mathbf{6}\mathbf{.}\mathbf{225}\mathbf{ }\mathit{k}\mathit{W}$