Mathematical Equations: The owner of a cargo ship has to decide how fast the ship should travel to deliver its cargo Custom Essay

This is the whole assessment details.
1) The owner of a cargo ship has to decide how fast the ship should travel to deliver its cargo. The ship is on a trip from Southampton to Lisbon. The distance between the ports is about 2,300 nautical miles.
The maximal speed of the freighter is 25 knots (nautical miles per hour).
The fixed expenses for operating the ship are £10,000 per day, and the income received for the trip is £120,000, independently of the time the trip takes.
In addition, the owner has to consider the fuel expenses.
The ship’s engine uses heavy crude, which costs £40.00 per 1,000 litres. However, the fuel consumption increases as the ship goes faster.
The equation which relates speed, k, to fuel consumption, c, is
c=200+400e^(k/(6 )) litres per hour
Calculate the optimal speed, using a graph to reinforce your calculations
2) The River Derwent flows into Peak Lake reservoir. The amount of water carried by the river depends on the season.
As a function of time, it is w(t)= 2+sin pt/180
Time t is measured in days, and t = 0 corresponds to January 1st. The units of w(t) are in M3 x 103 of water per day.
Water is released from Peak Lake at a constant rate of 2000m3 per day. At the beginning of the year, there are 2x105m3 of water in the reservoir.
‘ (a) How many cubic metres of water will there be in Peak Lake at t = 90?
(b) Find a function F(t) which tells how much water there is in the reservoir at any day of the year.
(c) At which rate does the amount of water in the reservoir change at the beginning of September?
d) On which days will there be 2.5 x105m3 of water in Peak Lake?
(e) What is the maximum volume of water held by the lake?
(f) On average, by how much has the amount of water in Peak Lake increased per day during the first three months of the year?
3) A mechanism drives a press tool along a displacement curve which follows the equation
S=1.6+tan?[cos?? (v(?^4-2?+4) )?]
a) Produce a graph of the displacement S cm against angular rotation ? rad between -3 = ? = 3

b) Differentiate the equation to produce an equation to find the velocity of the press tool at an angular velocity of (i) 1 rad/s. (ii) 6 rad/s

c) Plot the velocity curve between the same limits for ?

4) A single-cylinder model aircraft engine has a piston of 22mm diameter and a crankshaft radius of 10mm. The rod connecting the crankshaft to the piston has a length of 28mm

a) Produce an equation for the instantaneous piston displacement, S with respect to crankshaft angle ?

b) Differentate this equation to produce an equation for piston velocity and plot a graph of velocity against crankshaft position at a rotation speed of 300revs/second

c) Differentiate the velocity equation to produce an equation for acceleration and plot a graph of acceleration against crankshaft position at the same speed.
eading Materials

Module lecture and support notes.
See also module reading list.
Note: These sources are guides only to commonly available material. Students will also be expected to consult other relevant source material.

Stroud, K and Booth, D (2011) Advanced Engineering Mathematics Palgrave Macmillan
Kreyszig, E (2010) Advanced Engineering Mathematics Wiley
Bird, J (2010)_Higher Engineering Mathematics Newnes
Singh, K (2003) Engineering Mathematics through Applications Palgrave Macmillan

Submission Requirements

The assignment will need to be the equivalent of 800 words in length, plus diagrams, and conform to the appropriate written assignment standard.

 

You can place an order similar to this with us. You are assured of an authentic custom paper delivered within the given deadline besides our 24/7 customer support all through.

 

[order_calculator]