a rocket is moving along a curve with its equation given by s=2t^3-24t+s(s in meter and t in second).

find the time required for the rocket to reach a velocity of 126 m/s from its initial condition at t=0

the acceleration of the rocket when v=0 m/s

the net displacement during the interval from t=1 s to t=4 s

draw the graphs for displacement, velocity and acceleration and explain them.

The velocity of steam at inlet to a simple impulse turbine is 1200 m/s and the nozzle angle is 21°. The blade speed is 500 m/s and the blades are symmetrical. Evaluate:

1. The blade angles if the steam is to enter the blades without shock. If the friction effects on the blade are negligible, specify the tangential force on the blades and the diagram power for a mass flow of 0.85 kg/s. What are the axial thrust and the diagram efficiency?
2. If the relative velocity at exit is reduced by friction to 77 % of that at inlet, what are then the diagram power and the axial thrust? Evaluate also the diagram efficiency in this case.

1. A thick metal plate (alpha = 3.5 x 10^-6 m²/s and k = 0.7 W/m-K), initially at a uniform temperature of 100^oC, is suddenly exposed to a convection environment of water at 20^oC, giving a very large convection coefficient.

a. Sketch the surface heat flux, q", as a function of time

b. Using an explicit numerical scheme with a time step of 60 s, calculate the time required for the temperature to change 80 mm from the surface.

Discuss the difference between the ideal and the actual indicator diagrams of four stroke SI engine.

Identify five mechanical properties of materials which can be used to describe their behaviour as a result of applied external and internal forces. For each of the properties you identified,answer the following questions:
a. Describe the mechanical property in relation to type of material.
b. Discuss the application of the mechanical property in design of a named machined component or structure.
c. What are the effects of moisture content of the material on the mechanical property
d. What is the effect of extreme temperatures (too low or too high) on the property.

7.11 Consider two cases involving parallel flow of dry air at V = 1 m/s, T_∞ = 45°C, and atmospheric pressure over an isothermal plate at T_s = 20°C. In the first case, Re_x,c = 5 × 10⁵, while in the second case the flow is tripped to a turbulent state at x = 0 m. At what x‐location are the thermal boundary layer thicknesses of the two cases equal? What are the local heat fluxes at this location for the two cases?

Answer: x=.142; q”_lam = -129 W/m²;  q”_turb = -175 W/m²

Explain the concept of First Law of Thermodynamics in the following applications: (i) Human metabolism (ii) Launching the rocket (iii) Internal combustion engine

7.21 The Weather Channel reports that it is a hot, muggy day with an air temperature of 90°F, a 10 mph breeze out of the southwest, and bright sunshine with a solar insolation of 400 W/m². Consider the wall of a metal building over which the prevailing wind blows. The length of the wall in the wind direction is 10 m, and the emissivity is 0.93. Assume that all the solar irradiation is absorbed, that the surroundings are at T_sur = 85°F, and that flow is fully turbulent over the wall. Estimate the average wall temperature.

Answer: 53C

An exhaust fan systems consists of 4 parallel v-belts wrapped around driver pulleys A and driven pulley B with a diameter of 100 mm and 240 mm respectively. Coefficient of friction, μ between belt and pulleys is known as 0.25. Pulley groove, α has been design at an angle of 60°. The maximum permissible tension is 3860 N, cross-sectional area of the belt is A = 160 mm2 and density of belt’s material ρ = 1000 kg/m3. If the driver pulley A and driven pulley B rotates at a speed of 1800 RPM and 700 RPM individually due to slippages.

(i) Find the angle of contact of pulley A, given the pulley centre to centre distance is 1000 mm.

(ii) Calculate the tension distributed by centrifugal forces in one V-belt.

(iii) Deduce total power transmitted by the driver pulley A. (iv) Deduce total power received by the driven pulley B. (v) Find the belt slip percentage at pulley B

Problem 1: Carbon dioxide flows isentropically at the rate of 1 kg/s through a
convergent-divergent nozzle. The stagnation temperature is 310 K and the stagnation
pressure is 1400 kPa. If the exit pressure is 101.3 kPa, determine a) throat area, b) exit
Mach number and c) exit velocity. Assume sonic (M =1) conditions at throat.
(d) plot using MS excel variation of: total temperature, total pressure, total density,
density, temperature, Mach number, velocity, speed of sound along the centre line of

Problem 4: A solid-propellant rocket has the following data: Combustion chamber
temperature = 2600 K, Combustion chamber pressure = 20 MPa. The combustion
gasses flow isentropically through a convergent-divergent nozzle with Throat
diameter = 46 mm, The Exhaust gas constant R = 400 J/(kg · K) with Gas specific
heat ratio γ = 1.2. The Exit pressure = 100 kPa. Calculate: Exit Mach number,
velocity, and mass flow rate.

A room in the summer is to be maintained at 20°C, 50% RH when the outside conditions are 35°C, 80% saturation. The sensible and latent heat gains are 5.5 kW and 1.4 kW respectively. The conditioned air is supplied through ducks from a central station consisting of a cooler battery, a reheat battery, and a fan. Fresh air is supplied to a mixing unit where it mixes with a certain percentage of air recirculated from the room, the remainder of the room air being expelled to atmosphere. The air entering the room is at 13°C, the air temperature rise in the fan and duck work is 1°C, the air leaving the cooler battery and entering the reheat battery is at 8°C, and the apparatus dew point of the cooler is 2°C. Calculate (a) the cooler battery load in kW, (b) the reheater battery load in kW, (c) the cooler battery bypass factor.

A well-insulated expansion/throttle valve is designed to operate with refrigerant R134a. It receives a liquid-gas mixture with a quality of 0.1 and a pressure of 400 kPa. The refrigerant leaves with a pressure of 100 kPa. Find the temperature (in Celsius) and the specific volume (m3/kg) at the exit of the valve.