Question

A fountain shoots water to an height of 12 cm. from a nozzle of 0.60 diameter.
The pump at the base of the structure (which is 1.1 mts underneath the nozzle described above), pushes the water in a pipe of 1.2 cm diameter up to the nozzle at the top.
Calculate what is the relative pressure that the pump has to exert and also the pressure in case the liquid is considered viscous (viscosity=0.89x10*-3 Pascals)

Answer 1

We use the Bernoulli equation
P_1+ρgh_1+1/2 ρv_1^2=P_2+ρgh_2+1/2 ρv_2^2
v1=velocity at the pump
v2=velocity at the nozzle point on the ground
1/2 mv_2^2=mgh
v_2=√2gh
v_2=1.5 m/s
Then we find the volume flow rate
A_1=πr^2=3.14×(0.006/2)^2=0.283×〖10〗^(-4) m^2
A_2=πr^2=3.14×(0.012/2)^2=1.13×〖10〗^(-4) m^2
A_1 v_1=A_2 v_2
v_1=(A_2 v_2)/A_1
v_1=6.12 m/s
h2 = 0, P2 =101325 Pa
P_1=P_2+1/2 ρv_2^2-1/2 ρv_1^2
P_1=101325 Pa+1/2×1000 kg/m^3 ×(1.5 m/s)^2-1/2×1000 kg/m^3 ×(6.2 m/s)^2=83.738 kPa