Question: A 250-V, 4-pole, wave-wound d.c. series motor has 782 conductors on itsarmature. It has armature and series field resistance of 0.75 ohm. The motor takesa current of 40 A. Estimate its speed and gross torque developed if it has a flux per pole of 25 mWb Answer: Step 1 Mechanical Engineering homework question answer, step 1, image 1 Mechanical Engineering homework question answer, step 1, image 2 Step 2 Mechanical Engineering homework question answer, step 2, image 1 Step 3 Mechanical Engineering homework question answer, step 3, image 1

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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, $P_l=\mathbf{6}\mathbf{.}\mathbf{225}\mathbf{ }\mathit{k}\mathit{W}$