Answer Happy

• The pump must supply power (a) to accelerate the fluid entering the hose, (b) to lift fluid up to the jet pack and (c) to overcome frictional losses in the delivery pipe. Find expressions for each of these and evaluate them for the parameters you have chosen and the flow rate and frictional head loss you have found. What total pumping power is required, noting the likely efficiency of a centrifugal pump given in Technical tips'? (7 marks) Evaluation (5 marks) . In the light of your analysis, discuss the practicalities of the solution that you are analysing. You should look at two or three of cost, safety, robustness, size, noise, or any other factor you think interesting and relevant. (3 marks) • Finish by advising the company whether or not, in your opinion, it is worth taking this solution on to a detailed design/feasibility stage. (2 marks) You may draw on the ideas of others, but these should be properly acknowledged, and the analysis and evaluation should be wholly your own work. Technical tips: water jets . Review Week 16 material, and in particular Print Example 12.6: Reversal of direction of a free jet (Chapter 12, pp. 272-3) o Online Activities 16.3a to 16.3c: Restraining force on a fire hose nozzle (Study session 16.3). . Force arises from net momentum flux and boundary pressure forces. Can either of these be neglected? • A high-pressure fire hose with 100 mm internal diameter weighs 1050 g m-¹. The interior surface has a roughness of 0.05 mm. • The column of water in the hose will be supported from below, but the pipe itself needs to be lifted into the air. -3 and kinematic If needed, assume that seawater has density p = 1025 kg m viscosity v = 1.06 x 10-6 m² s1 at 20 °C. It is reasonable to expect 80% efficiency from a centrifugal water pump.


Detailed design (25 marks) . State the numerical parameters that you will use in your analysis. A maximum passenger mass of 100 kg and a minimum ride height of 30 m are given, so you should add estimates of equipment mass and hose layout to find the total mass to be lifted and the total length of hose needed. (2 marks) . Figure 3 shows a simplified outline of a water jet-pack head. Explain briefly (in around 150 words) how momentum and pressure effects can result in a force on the system, and why the pressure effects can be safely ignored. (3 marks) flying platform handheld stabiliser main thruster main thruster fire hose Figure 3 Simplified outline of a water jet-pack head (the small stabilising nozzles can be ignored in the analysis) Show that the vertical force F, produced by the momentum effects can be written as 1 F₁ = priz + 1 nAout Ain where Ain is the hose area, Aout is the thruster area, 7 is the number of thrusters, Vis the volumetric flow rate and p is the water density. (3 marks) Describe in words the effect on the required flow rate of increasing (a) the mass to be lifted, (b) the number of nozzles and (c) the size of each nozzle, each time keeping all other values constant (50 words for each point should be enough). (3 marks) . Assuming that 100 mm diameter fire hose is used - see the 'Technical tips' box below- find Ain Choose values for Aout and n, and use them to find the flow rate V that is required. (3 marks) . Use the d'Arcy-Welsbach equation and either the Moody diagram or the Moody calculator to find the head loss in the supply hose for the flow rate you have calculated. (4 marks)
The design brief Parascending behind speedboats is a popular thrill activity at beach resorts in warm countries, but it is noisy, requires a lot of space, puts fast-moving boats in close proximity to bathers, has a slow turnaround and depends on the use of fossil fuels. You have been asked to advise a company that is developing a new family fun ride for use in beach resorts in warm countries. This ride is intended to be a sustainable replacement for parascending that addresses as many of the current problems as possible. A single person of up to 100 kg is to be lifted to at least 30 m above sea level, using renewable electrical power. A possible solution has been identified: using a water jet pack powered by an electric seawater pump ashore (Figure 2). You have been asked to examine this idea and write a short technical report to the company, concentrating on the engineering requirements and recommending whether or not the solution is worth pursuing further. Figure 2 Using a water jet pack