physics problem?

Question

Hydrostatics and hydrodyamics?
1. In a hydraulic pressure the small cyclinder has a diameter of 5 cm ,while the large piston has a diameter of 10 cm.Neglecting friction,if a force of 15 N is applied to the small piston.what is the force on the large piston?

2. A cube 1 meter on one side floats half submerged in a tank of oil( specific gravity of 0.8) a.) What is the buoyant force exerted by oil acting on the cube? b.) If a piece of metal is placed on top of the cube, how heavy should the metal be in order to just submerge the cube completely?

3. a horizontal pipe 5 cm in radius at one end gradually decreases in size so that it is 2 cm in radius at the other end.the pipe is 5 m long.Water is pumped into the large end of the pipe at a speed of 2 m/s and a pressure of 8x10^5 N/m^2.Determine the speed and pressure of the water at the pipe's small end.

please help to sove this problem,i really appreciate your help

Answer 1

1)
Force / Area = Pressure
For same pressure applied to small cylinder and large piston.
F1/A1 = F2/A2
15 / (pi (5/2)^2) = F2 / (pi (10/2)^2)
Force on large piston, F2 = 60 N

2)
Specific gravity of oil = 800 kg/m^3 (0.8)
If half of cube submerged in a tank of oil,
volume of cube in oil = (1)(1)(0.5)= 0.5 m^3
buoyant force on cube
= (800)(9.81)(0.5)
= 3924 N

Weight of cube = 3924N

For weight of metal to submerge cube completely
volume of cube in oil = 1 m^3
weight of metal + weight of cube = buoyant force
mg + 3924N = (800)(9.81)(1)
mg = 3924 N
m = 400 kg

3)
Pressure x Area (large end) = Pressure x Area (small end)
(8 x 10^5) x (pi x 0.05^2) = P2 x (pi x 0.02^2)
Pressure of water at small end
= 5 x 10^6 N/m^2

Density Water x Specific Gravity x Area x Speed (large end)
= Density Water x Specific Gravity x Area x Speed (small end)
Area x Speed (large end) = Area x Speed (small end)
(pi x 0.05^2) x (2) = (pi x 0.02^2) x v
v = 12.5 m/s

Answer 2

i think first and second parts are answered
3
continuty equation: Av=constant
hence R(1)^2 *v(1)=R(2)^2 * v(2)
use this to find v(2) whenR(2)=2

now use bernoullies equation
1/2dv^2+dgh+P=constant

Answer 3

next time shorten yore question i'll try to answer it if i can.''