which states that the thermodynamics of a certain constant will be amplified by the force of the natural gravitational acceleration Eq. only holds if vs is below a certain critical value, which usually is determined by the diameter of the flow channel. In classical mechanics the force is often the gradient of a potential energy. Eq. shows that, in the case of the superfluid component, the force contains a term due to the gradient of the chemical potential. This is the origin of the remarkable properties of He-II such as the fountain effect. Fountain pressure In order to rewrite Eq. in more familiar form we use the general formula Here Sm is the molar entropy and Vm the molar volume. With Eq. μ(p,T) can be found by a line integration in the p-T plane. First we integrate from the origin (0,0) to (p,0), so at T =0. Next we integrate from (p,0) to (p,T), so with constant pressure (see figure 6). In the first integral dT=0 and in the second dp=0. With Eq. we obtain We are interested only in cases where p is small so that Vm is practically constant. So where Vm0 is the molar volume of the liquid at T =0 and p =0. The other term in Eq. is also written as a product of Vm0 and a quantity pf which has the dimension of pressure The pressure pf is called the fountain pressure. It can be calculated from the entropy of 4He which, in turn, can be calculated from the heat capacity. For T =Tλ the fountain pressure is equal to 0.692 bar. With a density of liquid helium of 125 kg/m3 and g = 9.8 m/s2 this corresponds with a liquid-helium column of 56 meter height. So, in many experiments, the fountain pressure has a bigger effect on the motion of the superfluid helium than gravity. With Eqs. and , Eq. obtains the form Substitution of Eq. in gives with ρ0 = M4/Vm0 the density of liquid 4He at zero pressure and temperature. Eq. shows that the superfluid component is accelerated by gradients in the pressure and in the gravitational field, as usual, but also by a gradient in the fountain pressure. So far Eq. has only mathematical meaning, but in special experimental arrangements pf can show up as a real pressure. Figure 7 shows two vessels both containing He-II. The left vessel is