# Hydraulic Pumps

 Question 1
A pump with an efficiency of 80% is used to draw groundwater from a well for irrigating a flat field of area 108 hectares. The base period and delta for paddy crop on this field are 120 days and 144 cm, respectively. Water application efficiency in the field is 80%. The lowest level of water in the well is 10 m below the ground. The minimum required horse power (h.p.) of the pump is ________. (round off to two decimal places)
(Consider 1 h.p. = 746 W; unit weight of water = 9810 $N/m^3$)
 A 25.64 B 36.25 C 30.82 D 48.32
GATE CE 2022 SET-2   Fluid Mechanics and Hydraulics
Question 1 Explanation:
Base period (B) = 120 days
\begin{aligned} Delta (\Delta )&=144 cm=1.44m\\ Duty(D)&=\frac{8.64B}{\Delta }=\frac{8.64 \times 120}{1.44}\\ D&=720\frac{hec}{cumec}\\ Q&=\frac{Area}{D}=\frac{108}{720}=\frac{3}{20}m^3/s\\ Q_{applied}&=\frac{Q}{\eta _a}=\frac{3}{20 \times 0.8}=\frac{3}{16}\\ \text{Power required}&=\frac{mgh}{t}\\ &=\rho _w \times \left ( \frac{volume}{t} \right )g \times h\\ &=\rho _w Qgh=\gamma Qh\\ &=9810 \times \frac{3}{16} \times 10\\ &=\frac{73575}{4}watt \end{aligned}
Horse power of pump $= \frac{\text{Power required}}{746 \times \text{efficiency}}=\frac{73575}{4 \times 746 \times 0.8}=30.82hp$
 Question 2
If a centrifugal pump has an impeller speed of N (in rpm), discharge Q (in $m^{3}/s$ ) and the total head H (in m), the expression for the specific speed $N_{s}$ of the pump is given by
 A $N_{s}=\frac{NQ^{0.5}}{H^{0.5}}$ B $N_{s}=\frac{NQ^{0.5}}{H}$ C $N_{s}=\frac{NQ^{0.5}}{H^{0.75}}$ D $N_{s}=\frac{NQ}{H^{0.75}}$
GATE CE 2017 SET-2   Fluid Mechanics and Hydraulics
Question 2 Explanation:
Specific speed of pump.
$N_{\mathrm{s}}=\frac{N \sqrt{Q}}{H^{3 / 4}}=\frac{N Q^{0.5}}{H^{0.75} }$

 Question 3
Identify the FALSE statement from the following:
The specific speed of the pump increases with
 A increase in shaft speed B increase in discharge C decrease in gravitational acceleration D increase in head
GATE CE 2006   Fluid Mechanics and Hydraulics
Question 3 Explanation:
The specific speed of a pump is given by,
$N_{S}=\frac{N \sqrt{Q}}{\left(H_{m}\right)^{3 / 4}}$
 Question 4
The allowable Net Positive Sustion Head (NPSH) for a pump provided by the manufacturer for a flow of 0.05 $m^{3}$/s is 3.3 m. The temperature of water is $30^{\circ}C$ (vapour pressure head absolute = 0.44 m), atmosphere pressure is 100 kPa absolute and the head loss from the reservoir to pump is 0.3 N-m/N. The maximum height of the pump above the sustion reservoir is
 A 10.19 m B 6.89 m C 6.15 m D 2.86 m
GATE CE 2004   Fluid Mechanics and Hydraulics
Question 4 Explanation:
The maximum suction lift,
\begin{aligned} h_{s}&=\left(\frac{p_{a}-p_{v}}{\gamma_{w}}\right)-N P S H-h_{ts} \\ p_{a} &=100 k P a_{i} \\ \gamma_{w} &=1000 \times 9.81=9810 \mathrm{N} / \mathrm{m}^{3} \\ \frac{p_{v}}{\gamma_{w}} &=0.44 \mathrm{m} \\ \frac{p_{a}}{\gamma_{w}} &=\frac{100 \times 10^{3}}{9810}=10.19 \mathrm{m} \\ \therefore \quad h_{s} &=10.19-0.44-3.3-0.3 \\ &=6.15 \mathrm{m} \end{aligned}
 Question 5
A pump can lift water at a discharge of 0.15$m^{3}/s$ to a head of 25 m. The critical cavitation number ($\sigma _{c}$) for the pump is found to be 0.144. The pump is to be installed at a location where the barometric pressure is 9.8 m of water and the vapour pressure of water is 0.30 of water. The intake pipe friction loss is 0.40 m. Using the minimum value of NPSH (Net Positive Suction Head), the maximum allowable elevation above the sump water surface at which the pump can be located is
 A 9.8m B 6.2m C 5.5m D none of these
GATE CE 2002   Fluid Mechanics and Hydraulics
Question 5 Explanation:
\begin{aligned} \sigma_{c} &=\text { NPSH/H } \\ \therefore \quad 0.144 &=\frac{\text { NPSH }}{25} \\ \therefore \quad \text { NPSH } &=3.6 \mathrm{m} \\ \text { NPSH } &=H_{\text {atm }}-H_{v}-h_{s}-h_{L} \\ 3.6 &=9.8-0.3-h_{s}-0.4 \\ \therefore \quad h_{s} &=5.5 \mathrm{m} \end{aligned}

There are 5 questions to complete.