Heloo Roger,
Alistairs analysis is only right if you don't change the pump, under these circumstance to increase the pressure at the outlet you need to restrict the outlet, its the thumb on the hose to make water squirt further but with less quanitity.
The relationship between pressure and flow is not always straightforward, and it relies on a number of other characteristics that need to be considered. Most pumps are quoted as having two figures that represent the two extremes of their performance. The maximum flow in L/m is with no hose connected to the pump, so in practice will never be achieved in a caravan.
The second is the maximum pressure, which is the pressure in Bar the pump can make when the flow is completely blocked, again of little practical use as there is no water flow, but it may be important if you have a pressure switched system. It is also important, because if the pump cannot cause the pressure switch to operate, the pump motor will continue to run, with the very real danger it will over heat (as there is no water flow to cool it) and damage its shaft seals causing irreparable damage.
It would be nice if a graph of flow against pressure were a straight line, but it isn't, each design of pump will have its own unique curved line, so what is true for one pump cannot be assumed to be the same for all, but the 'A typical' characteristic for a given system is to double the flow you need four times the pressure pr an inverse square law.
This means that the maximum flow rate of pump is rapidly reduces as soon as you add any pipework or other restrictions.
To put this into perspective, if you have a pump that claims a maximum flow of 10L/m and a max pressure of 1.2Bar it is likely that due to the height the water has to be raised from the water container to the kitchen sink and the restrictions of pipework and fittings the flow rate is likely to have dropped to about 4L/m, the additional height of the shower head and all its pipework and fittings the flow there is unlikely to exceed 1.5L/m.
Bearing in mind the inverse square law of the flow verses pressure graph, using a pump with a 1.4B output pressure (assuming all other things are equal) the difference at the shower will be minimal,
It would be foolhardy to try to use a pump with an even greater output pressure as the caravan pipe work will not stand anything above 1.5B and most water heaters have pressure relief system that will opera e and just dump water.
Its nice to hope that the systems in a caravan will give you the same performance ast those at home, but sadly in most cases they just cant. However if lower your expectations just a little the experience can be just as rewarding, and sometimes a little fun in finding ways to do things with less in knowledge you are actually helping to reduce waste.