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ULTRAFLOW® 54/34
34
Kamstrup A/S · Technical description · 5512-2464_A1_GB_08.2019
This can be explained by combining Bernoulli’s equation and the continuity equation. Based on Bernoulli's equation
, the
total pressure of the flow will be the same for any cross section. It can be reduced to:
𝑝
𝑠𝑡𝑎𝑡.
+ 𝑝
𝑑𝑦𝑛𝑎𝑚.
= 𝑝
𝑠𝑡𝑎𝑡.
+
1
2
𝜌𝑣
2
= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
(Bernoulli’s equation)
𝑝
𝑠𝑡𝑎𝑡.
is the static pressure.
[𝑃𝑎 =
𝑁
𝑚
2
=
𝑘𝑔
𝑠
2
∙𝑚
] ; 1 𝑏𝑎𝑟 = 10
5 𝑁
𝑚
2
𝑝
𝑑𝑦𝑛𝑎𝑚.
is the dynamic pressure.
[𝑃𝑎 =
𝑁
𝑚
2
=
𝑘𝑔
𝑠
2
∙𝑚
]; 1 𝑏𝑎𝑟 = 10
5 𝑁
𝑚
2
𝜌
is the water density.
[
𝑘𝑔
𝑚
3
]
𝑣
is the water flow rate.
[
𝑚
𝑠
]
The continuity equation determines that the product of pipe cross sectional area
𝐴
and average flow velocity
𝑣
, which
corresponds to the volume flow rate passing through, is constant for an incompressible fluid like e.g. water. Therefore,
the flow velocity is increased in a contraction and the static pressure decreases.
𝑞 = 𝐴
1
∙ 𝑣
1
= 𝐴
2
∙ 𝑣
2
= ⋯ = 𝐴
𝑖
∙ 𝑣
𝑖
= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
(Continuity equation)
When dimensioning a flow sensor, you must take the above into consideration, especially if the sensor is used within the
scope of EN 1434 between q
p
and q
s
, and in case of major pipe contractions.