What is the needed flow rate of the impeller with this info?

[Max KL]

Hi everyone!

As an experiment I am trying to calculate building my own PWC similar to a jetski assuming it is for sea level use. I really appreciate all detailed answers as I want to understand. The impeller will be installed under rear of craft, engine is mounted on top.

Given Information:

Total craft mass: 100kg including 1 person.

Dimensions: 200cm x 60cm x 10cm thick (Exact hull design is not sure; similar to jet ski or surfboard.)

Water density: 1,000kg/m3.

Acceleration: 0 – 12m/s in 5s.

Top speed: 12m/s

Impeller housing diameter: 10cm. (Impeller design/ pitch depends on the answer to the question.. ?)

To achieve the given acceleration & top speed, What is the needed flow rate in liters / second & needed torque in Newton metres of the impeller?

Now just to get started I understand the momentum of the impellers thrust must be equal to the momentum of the craft moving forward. (conservation of momentum)

So, 1200kg * m/s is the momentum of the craft (assuming 0 drag force) How is drag calculated assuming I don’t know to what extent this craft will start planing? An average is what I am looking for. Weight distribution/ center of gravity is at rear of craft.

Please understand I’m a beginner at physics, I appreciate all answers as I really want to learn and also any corrections if I'm wrong. Thanks !

Max

 

[SteamKing]

Hi everyone!

As an experiment I am trying to calculate building my own PWC similar to a jetski assuming it is for sea level use. I really appreciate all detailed answers as I want to understand. The impeller will be installed under rear of craft, engine is mounted on top.

Given Information:

Total craft mass: 100kg including 1 person.

This had be a very small person driving this craft, otherwise there is no mass available for the PWC you are designing. The mass of an adult human ranges from 60-80 kg.

https://en.wikipedia.org/wiki/Human_body_weight

 

[Max KL]

This had be a very small person driving this craft, otherwise there is no mass available for the PWC you are designing. The mass of an adult human ranges from 60-80 kg.

https://en.wikipedia.org/wiki/Human_body_weight

Yes true! It is supposed to be very light not more than 10 - 15kg that's why i averaged assumption of total mass at 100kg.

 

[billy_joule]

Google "wavejet" for something similar.
We've dismantled one at my work, it has two high end rc bldc motors powering two ~50mm ID jets, two 300Wh Li ion batteries.
It weighs over 10kg and performance is miles bellow what you want, unless you're happy with a runtime of just a couple minutes?

 

[Max KL]

Thanks billy_joule,
I have seen wavejets what's the acceleration or top speed like? I'm looking forward to power it with a fuel engine to have more power but runtime of at least 30mins would be fine if it were powered by LI ion batteries.

 

[billy_joule]

Thanks billy_joule,
I have seen wavejets what's the acceleration or top speed like?

Pretty pitiful, slower acceleration than a surfer paddling and top speed about the same as a surfer.
The motors consume about 800W electrical power. After losses, I'd guess maybe 400W or so make it to propulsive power.

Trying to design a PWC from first principles is incredibly hard, especially for a non-engineer.
I'd recommend just looking at existing designs, looking at the performance, power, weight, size, shape, etc etc of small jet skis, large RC craft, powered surfboards, kayaks, dinghies etc etc. should give you a pretty good idea of what power levels you'll need.

Getting 30 min runtime with your weight constraint rules out batteries, their energy density is way too low. You'll need a highly tuned, low weight (ergo; short lived, unreliable) gas engine, I'm guessing you'd need something like this:
http://www.hobbyking.com/hobbyking/store/__33546__JC120_EVO_Gas_engine_Version_2_w_CD_Ignition_120cc_12_5hp_8_000rpm.html
and one of these:
http://www.mhz-powerboats.com/Jet/Jet-62.html
And a gearbox between them.

 

[CWatters]

Try getting someone to tow you behind a boat. By measuring the speed of the boat and the tension in the tow rope you can get an idea of the power required to go any speed you want or accelerate etc

 

[Max KL]

Thanks Cwatters,
Using the speed of the boat and the tension of the rope, what is the formula to calculate the power(thrust) required to reach a certain accel. / top speed?

 

[CWatters]

I would have them tow you at the highest speed you want. Then the power required is given by

Power = tension * velocity

Where..
Power is in Watts
Tension is in Newtons
Velocity is in Meters per second

This doesn't take into account the efficiency of the prop or motor so you need to divide by the efficiency. eg if the efficiency of the prop was say 80% (I've no idea!) then multiply the power calculated above by 100/80 to get the power needed at the prop. Likewise for the motor.

It's not quite so easy to work out the power required to accelerate to a particular speed in a particular time. Perhaps someone else can comment on that.