Principles of Hydraulics

Question 1

State the density of fresh water, sea water, light oil, glycerine and mercury.

Answer 1

w: 1000kgm^-3, sw: 1027kgm^-3, o:800kgm^-3, g: 1260khm^-3, m: 13,600kgm^-3

Question 2

What is specific weight?

Answer 2

w=fluid weight/ volume= mg/v= ρg (N/m^3)

Question 3

What is specific gravity?

Answer 3

s= (mass of fluid for specific volume) / (mass of water for same volume)

Question 4

What are the different units for pressure?

Answer 4

p= force/area. 1 pascal= 1 N/m^2. 1 bar = 1 atmosphere =100,000 N/m^2

Question 5

How do you calculate the bulk modulus (K)?

Answer 5

K=-VΔp/Δv. for water k=2.210^9

Question 6

How do you calculate the surface tension of a fluid (σ)?

Answer 6

σ=(ρgDh)/(4cos(θ)

θ-angle between wall and fluid, D-diameter of thin tube, h-height of fluid in thin tube

Question 7

How do you calculate the force on the base of a container due to a fluid?

Answer 7

F=ρgHA, as h increases pressure increases linearly at a rate of ρg

Question 8

Define Gauge (engineering) and Absolute pressure.

Answer 8

absolute pressure= atmospheric pressure (1*10^5) + ρgh

gauge pressure= ρgh -this is used for engineering calculations

Question 9

List 4 pressure measurement devices.

Answer 9

Barometer, Piezometer, Pressure Transducer, Manometer

Question 10

Why is an inclined monometer more accurate than a vertical one?

Answer 10

measuring over a larger distance so is more accurate.

Question 11

How do you calculate the force on a vertical wall due to a liquid?

Answer 11

F=ρgw[(H^2)/2] ,w-width of wall.

to calculate the force over a specific strip F=ρgw[(h^2)/2]^H0

Question 12

How do you locate the point of action of a resultant force?

Answer 12

Taking moments about a corner at the free surface: FL=ρgwH^3/3, L=2H/3
For a sloping wall: L=2H/3sin(x)

Question 13

How do you calculate the resultant force on a curved wall?

Answer 13

Obtain F(h) =(ρgwH^2)/2   and    F(v) =weight above the curve (ρgv)
F(resultant)^2 = F(h)^2 + F(v)^2
tan(θ)=F(v)/F(h)

Question 14

How do you locate the resultant on a curved surface?

Answer 14

F(h) acts 2H/3 , F(v) acts through the centroid of the area above the curve (x=4r/3π)
Large gates are normally circular in shape as the only applied moment needed to raise it is to counter the self weight.

Question 15

How do you calculate the buoyancy force on a fully submerged object?

Answer 15

B = ρgAD

A-plan area, D-height of the object, if the system is in equilibrium then B=W

Question 16

What is the concept of a metacentre?

Answer 16

the point of intersection between an imaginary line drawn vertically through the centre of buoyancy of a floating vessel and a corresponding line through the new centre of buoyancy when the vessel is tilted.

Question 17

How can you say whether a floating system is stable or not?

Answer 17

If the metacentre, m, is above the centre of mass, g, then the system is stable. (Bm>Bg)

Question 18

How do you calculate Bm and Bg?

Answer 18

Bm=I/V , I-second moment of area (bd^3/12) , v-displaced volume.
Bg= distance from centre of mass to new centre of buoyancy

Question 19

Define a streamline and a streamtube.

Answer 19

A streamline is a path that a small element of fluid has followed. If a surface is created of streamlines, it is possible to create a streamtube. In a small time period mass flowrate in = mass flowrate out. (ρvA) v-velocity

Question 20

What is the principle of mass continuity?

Answer 20

V(in)A(in) = V(out)A(out)

Question 21

How do you calculate the total amount of energy per unit weight of a fluid in a system?

Answer 21

H = p/ρg + v^2/2g + Z

no energy losses

Question 22

Describe the concept of a control volume

Answer 22

A control volume in an engineering system is a volume that does not change shape, no fluid crosses its boundaries except at its entry and exit surfaces.

Question 23

What two things do you need to know in order for a venturi meter to work?

Answer 23

(1) pipe and throat cross-sectional area.

(2) difference in pressure and elevation between the original pipe and the throat of the venturi meter.

Question 24

How do you calculate the flowrate of a fluid?

Answer 24

Q(actual) = CdVA
Cd- coefficient of discharge
V- velocity = ((2g(h(a)-h(b)))/[1-(A(b)^2/A(a)^2)]) -horizontal

Question 25

What is an orifice plate?

Answer 25

Orifice plates are normally circular and have a small sharp edged hole. The orifice plate is then inserted in a pipe and the fluid accelerates through the hole and pressure drops. Q=CvCca*V(2) -small orifices
Cv- coefficient of velocity accounts for energy loss

Question 26

How do you calculate the flowrate through a large orifice?

Answer 26

Can no longer assume constant velocity over the orifice.

Q = (2*(2g)^1/2)/3 * W[h(2)^3/2 - h(1)^3/2]

Question 27

How do you calculate discharge through a small orifice with a reducing free surface level?

Answer 27

Time to empty a tank T = (2AH^1/2)/(Cda(2g)^1/2)

Question 28

How do you calculate the forces involved in a control volume of a pipe?

Answer 28

Balance momentum forces against pressure forces + reaction forces, F(m) = F(p) + F(r). Do this for (x,y).
F(m)=ρQ(V(2)-V(1)) V(2/1)-velocity out/in