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Fluid Pressures
------=_NextPart_01C97CE4.AD3AF640 Content-Location: file:///C:/2D6C5513/7FluidPressures_files/slide0014.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
We are to calculate the total pressure exerted on a = flat plate submerged in water.
Fluid Pressures
------=_NextPart_01C97CE4.AD3AF640 Content-Location: file:///C:/2D6C5513/7FluidPressures_files/slide0015.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
We are to calculate the total pressure exerted on a = flat plate submerged in water.
Let A = =3D Area of the plate
h =3D= the depth
= 61; =3D the density of the fluid
A
h
ρ
Fluid Pressures
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We are to calculate the total pressure exerted on a = flat plate submerged in water.
Let A = =3D Area of the plate
h =3D= the depth
= 61; =3D the density of the fluid
The simplest case is when the pla= te is submerged horizontally in w= ater.
A
h
ρ
Fluid Pressures
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We are to calculate the total pressure exerted on a = flat plate submerged in water.
Let A = =3D Area of the plate
h =3D= the depth
= 61; =3D the density of the fluid
The simplest case is when the pla= te is submerged horizontally in w= ater.
A
h
ρ
The total pressure P on the plate is the weight of the <= span style=3D'font-size:156%'>volume of the water sits over the plate, <= /span>
Fluid Pressures
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We are to calculate the total pressure exerted on a = flat plate submerged in water.
Let A = =3D Area of the plate
h =3D= the depth
= 61; =3D the density of the fluid
The simplest case is when the pla= te is submerged horizontally in w= ater.
A
h
ρ
The total pressure P on the plate is the weight of the volume of the water sits over the plate, that is =
P =3D= ρAh <= /div>
Fluid Pressures
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We are to calculate the total pressure exerted on a = flat plate submerged in water.
Let A = =3D Area of the plate
h =3D= the depth
= 61; =3D the density of the fluid
The simplest case is when the pla= te is submerged horizontally in w= ater.
A
h
ρ
The total pressure P on the plate is the weight of the volume of the water sits over the plate, that is =
P =3D= ρAh <= /div>
We are to calculate the pressure exerted on plates of <= span style=3D'font-size:156%'>various shapes that sits vertically in water.
Fluid Pressures
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Suppose a plate is submerged in water vertically with the top of the plate is at a distance h to the surface.
ρ
h
Fluid Pressures
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Suppose a plate is submerged in water vertically with the top of the plate is at a distance h to the surface.
ρ
h
We select a direction and set the measurement x, say from the top x =3D 0 to the bottom x =3D b of the plate.
Fluid Pressures
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Suppose a plate is submerged in water vertically with the top of the plate is at a distance h to the surface.
ρ
h
We select a direction and set the measurement x, say from the top x =3D 0 to the bottom x =3D b of the plate.
x=3D0
x=3Db
Fluid Pressures
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------=_NextPart_01C97CE4.AD3AF640 Content-Location: file:///C:/2D6C5513/7FluidPressures_files/slide0058_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhhwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACC AAEAgAAAAAAAAAIXjAN5qJewXmxGOsrg1RXbzmVT+InbuBQAOx== ------=_NextPart_01C97CE4.AD3AF640 Content-Location: file:///C:/2D6C5513/7FluidPressures_files/slide0021.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Suppose a plate is submerged in water vertically with the top of the plate is at a distance h to the surface.
ρ
h
We select a direction and set the measurement x, say from the top x =3D 0 to the bottom x =3D b of the plate.
x=3D0
x=3Db
Let the sequence {0=3Dx0, x<= /span>1= , x2, ..= , xn= =3Db} be an equi- partition of [0, b].
Fluid Pressures
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------=_NextPart_01C97CE4.AD3AF640 Content-Location: file:///C:/2D6C5513/7FluidPressures_files/slide0021_image028.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhhwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACC AAEAgAAAAAAAAAIXjAN5qJewXmxGOsrg1RXbzmVT+InbuBQAOx== ------=_NextPart_01C97CE4.AD3AF640 Content-Location: file:///C:/2D6C5513/7FluidPressures_files/slide0055.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Suppose a plate is submerged in water vertically with the top of the plate is at a distance h to the surface.
ρ
h
We select a direction and set the measurement x, say from the top x =3D 0 to the bottom x =3D b of the plate.
x=3D0
x=3Db
Let the sequence {0=3Dx0, x<= /span>1= , x2, ..= , xn= =3Db} be an equi- partition of [0, b],
Fluid Pressures
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Suppose a plate is submerged in water vertically with the top of the plate is at a distance h to the surface.
ρ
h
We select a direction and set the measurement x, say from the top x =3D 0 to the bottom x =3D b of the plate.
x=3D0
x=3Db
Let the sequence {0=3Dx0, x<= /span>1= , x2, ..= , xn= =3Db} be an equi- partition of [0, b], and xi= –1 and= xi= two arbitrary points.
xi-1
xi
Fluid Pressures
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Suppose a plate is submerged in water vertically with the top of the plate is at a distance h to the surface.
ρ
h
We select a direction and set the measurement x, say from the top x =3D 0 to the bottom x =3D b of the plate.
x=3D0
x=3Db
xi-1
xi
Let L(x) =3D cross-sectional length at x, so = ;
L(xi) =3D cross-sectional length at xi.
Let the sequence {0=3Dx0, x<= /span>1= , x2, ..= , xn= =3Db} be an equi- partition of [0, b], and xi= –1 and= xi= two arbitrary points.
Fluid Pressures
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Suppose a plate is submerged in water vertically with the top of the plate is at a distance h to the surface.
ρ
h
We select a direction and set the measurement x, say from the top x =3D 0 to the bottom x =3D b of the plate.
x=3D0
x=3Db
xi-1
xi
L(xi)
Let L(x) =3D cross-sectional length at x, so = ;
L(xi) =3D cross-sectional length at xi.
Let the sequence {0=3Dx0, x<= /span>1= , x2, ..= , xn= =3Db} be an equi- partition of [0, b], and xi= –1 and= xi= two arbitrary points.
Fluid Pressures
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Suppose a plate is submerged in water vertically with the top of the plate is at a distance h to the surface.
ρ
h
We select a direction and set the measurement x, say from the top x =3D 0 to the bottom x =3D b of the plate.
x=3D0
x=3Db
xi-1
xi
L(xi)
Let L(x) =3D cross-sectional length at x, so = ;
L(xi) =3D cross-sectional length at xi.
Let the sequence {0=3Dx0, x<= /span>1= , x2, ..= , xn= =3Db} be an equi- partition of [0, b], and xi= –1 and= xi= two arbitrary points.
Let Δx =3D the length of each subinterval.
Fluid Pressures
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file:///C:/2D6C5513/7FluidPressures_files/slide0060_image070.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAAMAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAJ AAsAgAAAAP8AAAIMjI95wO0Po5xUqpsKADs= ------=_NextPart_01C97CE4.AD3AF640 Content-Location: file:///C:/2D6C5513/7FluidPressures_files/slide0061.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
Suppose a plate is submerged in water vertically with the top of the plate is at a distance h to the surface.
We select a direction and set the measurement x, say from the top x =3D 0 to the bottom x =3D b of the plate.
Let L(x) =3D cross-sectional length at x, so = ;
L(xi) =3D cross-sectional length at xi.
Let the sequence {0=3Dx0, x<= /span>1= , x2, ..= , xn= =3Db} be an equi- partition of [0, b], and xi= –1 and= xi= two arbitrary points.
Let Δx =3D the length of each subinterval.
ρ
h
x=3D0
x=3Db
xi-1
xi
L(xi)
Δ= x
Fluid Pressures
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ρ
h
x=3D0
x=3Db
xi-1
xi
L(xi)
The cross-sectional area from
xi-1 to xi is approximately L(xi)Δx.  
Δ= x
Fluid Pressures
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ρ
h
x=3D0
x=3Db
xi-1
xi
L(xi)
The cross-sectional area from
xi-1 to xi is approximately L(xi)Δx.  
So the cross-sectional area from
xi-1 to xi is approximately L(xi)Δx.  
Δ= x
h+xi= <= b>
Fluid Pressures
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ρ
h
x=3D0
x=3Db
xi-1
xi
L(xi)
The cross-sectional area from
xi-1 to xi is approximately L(xi)Δx.  
So the cross-sectional area from
xi-1 to xi is approximately L(xi)Δx.  
Δ= x
The depth of this strip of area is approximately (xi+h).  
h+xi= <= b>
Fluid Pressures
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AAsAgAAAAP8AAAIMjI95wO0Po5xUqpsKADs= ------=_NextPart_01C97CE4.AD3AF640 Content-Location: file:///C:/2D6C5513/7FluidPressures_files/slide0027.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
ρ
h
x=3D0
x=3Db
xi-1
xi
L(xi)
The cross-sectional area from
xi-1 to xi is approximately L(xi)Δx.  
So the cross-sectional area from
xi-1 to xi is approximately L(xi)Δx.  
Δ= x
So the fluid pressure exerted on
this strip of area is approximately ρL(xi= )(xi+h)Δx.  
The depth of this strip of area is approximately (xi+h).  
h+xi= <= b>
Fluid Pressures
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AAsAgAAAAP8AAAIMjI95wO0Po5xUqpsKADs= ------=_NextPart_01C97CE4.AD3AF640 Content-Location: file:///C:/2D6C5513/7FluidPressures_files/slide0028.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Slide 1
ρ
h
x=3D0
x=3Db
xi-1
xi
L(xi)
The cross-sectional area from
xi-1 to xi is approximately L(xi)Δx.  
So the cross-sectional area from
xi-1 to xi is approximately L(xi)Δx.  
Δ= x
So the fluid pressure exerted on
this strip of area is approximately ρL(xi= )(xi+h)Δx.  
The depth of this strip of area is approximately (xi+h).  
h+xi= <= b>
Hence t= he total fluid pressure P is:
ͨ= 1; ρL(xi= )(xi+h) = Δx  
P =3D = lim
n&agr= ave;∞
Fluid Pressures
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