Question 1 |

A jet of water having a velocity of 20 \mathrm{~m} / \mathrm{s} strikes a series of plats fixed radially on a wheel revolving in the same direction a the jet at 15 \mathrm{~m} / \mathrm{s}. What is the percentage efficiency of the plates ? (round off to one decimal place).

37.5 | |

66.7 | |

50 | |

88.9 |

Question 1 Explanation:

Given water jet velocity \left(V_{1}\right)=20 \mathrm{~m} / \mathrm{s}

Wheel velocity (u)=15 \mathrm{~m} / \mathrm{s}

F_{x}=\rho A V_{1}\left(V_{1}-u\right)

\% efficiency of the plates

\begin{aligned} & =\frac{F_{x} u \times 100}{\frac{1}{2} \rho Q V_{1}^{2}} \\ & =\frac{P \times Q\left(V_{1}-u\right) u \times 100}{\frac{1}{2} \rho Q V_{1}^{2}} \\ & =\frac{2\left(V_{1}-u\right) u \times 100}{V_{1}^{2}} \\ & =\frac{2(20-15) \times 15}{20^{2}} \times 100 \\ & =37.5 \% \end{aligned}

Wheel velocity (u)=15 \mathrm{~m} / \mathrm{s}

F_{x}=\rho A V_{1}\left(V_{1}-u\right)

\% efficiency of the plates

\begin{aligned} & =\frac{F_{x} u \times 100}{\frac{1}{2} \rho Q V_{1}^{2}} \\ & =\frac{P \times Q\left(V_{1}-u\right) u \times 100}{\frac{1}{2} \rho Q V_{1}^{2}} \\ & =\frac{2\left(V_{1}-u\right) u \times 100}{V_{1}^{2}} \\ & =\frac{2(20-15) \times 15}{20^{2}} \times 100 \\ & =37.5 \% \end{aligned}

Question 2 |

Consider the reactor shown in the figure. The flow rate through the reactor is Q \; m^3/h. The concentrations (in mg/L) of a compound in the influent and effluent are C_0 and C, respectively. The compound is degraded in the reactor following the first order reaction. The mixing condition of the reactor can be varied such that the reactor becomes either a completely mixed flow reactor (CMFR) or a plug-flow reactor (PFR). The length of the reactor can be adjusted in these two mixing conditions to L_{CMFR} and L_{PFR} while keeping the cross-section of the reactor constant. Assuming steady stateand for C/C_0 =0.8, the value of L_{CMFR}/L_{PFR} (round off to 2 decimal places) is _______

1.12 | |

1.85 | |

2.44 | |

2.97 |

Question 2 Explanation:

Hydrocarbons and nitrogen oxides are considered primary air pollutants.

c=\frac{c_0}{1+kt}

For (PFR) plug flow reactor

\begin{aligned} c&=c_0e^{-kt} \\ \text{As}\;\; c/c_0 &=0.8 \\ \text{For CMFR} \;\; 0.8&=\frac{1}{1+kt_{CMFR}} \\ \Rightarrow \;\;t_{CMFR} &=\frac{0.25}{k} \\ \text{For PFR} \;\; 0.8&=e^{-kt_{PFR}} \\ \Rightarrow \;\; t_{PFR}&=\frac{0.22314}{k} \end{aligned}

Now for steady state

\begin{aligned} v&=\text{constant}\\ L&=vt\\ So, \;\;\frac{L_{CMFR}}{L_{PFR}}&=\frac{vt_{CMFR}}{vt_{PFR}}\\ &=\frac{0.25}{0.22314}=1.12 \end{aligned}

c=\frac{c_0}{1+kt}

For (PFR) plug flow reactor

\begin{aligned} c&=c_0e^{-kt} \\ \text{As}\;\; c/c_0 &=0.8 \\ \text{For CMFR} \;\; 0.8&=\frac{1}{1+kt_{CMFR}} \\ \Rightarrow \;\;t_{CMFR} &=\frac{0.25}{k} \\ \text{For PFR} \;\; 0.8&=e^{-kt_{PFR}} \\ \Rightarrow \;\; t_{PFR}&=\frac{0.22314}{k} \end{aligned}

Now for steady state

\begin{aligned} v&=\text{constant}\\ L&=vt\\ So, \;\;\frac{L_{CMFR}}{L_{PFR}}&=\frac{vt_{CMFR}}{vt_{PFR}}\\ &=\frac{0.25}{0.22314}=1.12 \end{aligned}

Question 3 |

A penstock of 1 m diameter and 5 km length is used to supply water from a reservoir to an impulse turbine. A nozzle of 15 cm diameter is fixed at the end of the penstock. The elevation difference between the turbine and water level in the reservoir is 500 m. Consider the head loss due to friction as 5% of the velocity head available at the jet. Assume unit weight of water = 10\: kN/m^{3} and acceleration due to gravity (g)=10\: m/s^{2}. If the overall efficiency 80%, power generated (expressed in kW and rounded to nearest integer) is ___________

7570 | |

8212.5 | |

6570 | |

8874.8 |

Question 3 Explanation:

Apply energy equaiton at the free surlace of

reservior and exit of nozzle

\begin{aligned} 500&=\text{Head loss } \frac{v_{1}^{2}}{2 g}\\ 500&=0.05 \frac{v_{1}^{2}}{2 g}+\frac{v_{1}^{2}}{2 g}\\ \sqrt{\frac{2 \times 10 \times 500}{1.05}}&=v_{1} \\ V_{1}&=97.59 \mathrm{m} / \mathrm{sec}\\ \text{Water Power WP }\\ &=\frac{1}{2} m v_{1}^{2} \\ &=\frac{1}{2}\left(10^{2}\right) \times \frac{\pi}{4}(0.15)^{2}(9759) \\ &=8212178 \mathrm{kW} \\ \text{Now,}\quad \eta_{0}&=\frac{\text { Shaft power }(\$ P)}{W P} \\ 08&=\frac{S P}{8212178} \\ S P&=6569.74 \mathrm{kW} \\ &\simeq 6570 \mathrm{kW} \end{aligned}

reservior and exit of nozzle

\begin{aligned} 500&=\text{Head loss } \frac{v_{1}^{2}}{2 g}\\ 500&=0.05 \frac{v_{1}^{2}}{2 g}+\frac{v_{1}^{2}}{2 g}\\ \sqrt{\frac{2 \times 10 \times 500}{1.05}}&=v_{1} \\ V_{1}&=97.59 \mathrm{m} / \mathrm{sec}\\ \text{Water Power WP }\\ &=\frac{1}{2} m v_{1}^{2} \\ &=\frac{1}{2}\left(10^{2}\right) \times \frac{\pi}{4}(0.15)^{2}(9759) \\ &=8212178 \mathrm{kW} \\ \text{Now,}\quad \eta_{0}&=\frac{\text { Shaft power }(\$ P)}{W P} \\ 08&=\frac{S P}{8212178} \\ S P&=6569.74 \mathrm{kW} \\ &\simeq 6570 \mathrm{kW} \end{aligned}

Question 4 |

A square plate is suspended vertically from one of its edges using a hinge support as shown in figure. A water jet of 20 mm diameter having a velocity of 10 m/s strikes the plate at its mid-point, at an angle of 30^{\circ} with the vertical. Consider g as 9.81\: m/s^{2} and neglect the self-weight of the plate. The force F (expressed in N) required to keep the plate in its vertical position is _______________

7.85 | |

8.8 | |

6.63 | |

0.763 |

Question 4 Explanation:

Force exerted by jet in x direction

\begin{array}{l} F_{x}=m[V \sin \theta-0 \mid \\ =\rho Q \times V \sin \theta \\ =\rho A V \times V \sin \theta \\ =1000 \times \frac{\pi}{4}(0.02)^{2} \times(10)^{2} \sin 30^{\circ} \\ =157079 \mathrm{N} \end{array}

Taking mornent about hinge

\begin{array}{r} F_{x} \times \frac{0.2}{2}=F \times 02 \\ F=7.85 \mathrm{N} \end{array}

Question 5 |

A horizontal nozzle of 30 mm diameter discharges a steady jet of water into the atmosphere at a rate of 15 liters per second. The diameter of inlet to the nozzle is 100 mm. The jet Impinges normal to a flat stationary plate held close to the nozzle end. Neglecting air friction and considering the density of water as 1000 kg/m^3, force exerted by the jet (in N) on the plate is _______

318.3 | |

328.3 | |

246.8 | |

338.3 |

Question 5 Explanation:

\text{Force }=\rho a V^{2}

\mathrm{Q}=\mathrm{a} \mathrm{V}=15 \; litre/sec (given)

\text{Force }=\rho \frac{\mathrm{Q}^{2}}{\mathrm{a}}

=1000 \times \frac{15^{2}}{\pi} \times 30^{2} \mathrm{m}^{3} \times 10^{-6} \frac{\mathrm{m}^{6}}{\mathrm{s}^{2}} \times \frac{1}{10^{-6}} \mathrm{m}^{2}

=1000 \times \frac{1}{\pi} \mathrm{N}=318.3 \mathrm{N}

\mathrm{Q}=\mathrm{a} \mathrm{V}=15 \; litre/sec (given)

\text{Force }=\rho \frac{\mathrm{Q}^{2}}{\mathrm{a}}

=1000 \times \frac{15^{2}}{\pi} \times 30^{2} \mathrm{m}^{3} \times 10^{-6} \frac{\mathrm{m}^{6}}{\mathrm{s}^{2}} \times \frac{1}{10^{-6}} \mathrm{m}^{2}

=1000 \times \frac{1}{\pi} \mathrm{N}=318.3 \mathrm{N}

There are 5 questions to complete.