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Hydrostatic Level Calculation: Density, Pressure Units and Sensor Offset

Calculate liquid-column height from gauge pressure using consistent SI units, then relate it to the tank datum. Separate density assumptions, sensor elevation and volume conversion with worked examples.

Define the scope before using the formula

This guide concerns a liquid at rest, of known uniform density, in an open or effectively vented vessel, with gauge pressure referenced to the same atmosphere as the liquid surface. WIKA's technical explanation relates hydrostatic pressure to liquid-column height and density. A pressurised vessel, a changing density profile or a different pressure reference needs a separately reviewed method. Do not apply the simplified formula to an arbitrary pressure reading.

Keep the units consistent

Use h = p / (ρ × g), where h is height above the sensing diaphragm in metres, p is gauge pressure in pascals, ρ is mass density in kg/m³, and g is gravitational acceleration in m/s². Convert pressure before calculating: 1 kPa = 1,000 Pa and 1 bar = 100,000 Pa. The result is a length, not a volume. A pressure label in metres of water column also needs its stated density and gravity convention; it is not automatically the height of every liquid.

Example 1: liquid-column height and the tank datum

The following are hypothetical arithmetic inputs, not a WESIVO range, accuracy claim or installation recommendation. Set ρ = 1,000 kg/m³ and g = 9.80665 m/s² for this example. At p = 11,767.98 Pa, h = 11,767.98 / (1,000 × 9.80665) = 1.20 m above the diaphragm.

Define z as the diaphragm elevation above the chosen tank-floor datum. If z = 0.30 m and the diaphragm is submerged, the surface elevation relative to that datum is H = z + h = 1.50 m. Keep the sign convention on the drawing. A probe above the floor cannot provide the same submerged-column measurement after the surface falls below its diaphragm; adding an offset does not create measurement coverage there.

Example 2: an incorrect density setting changes the result

In a separate hypothetical case, let the actual uniform density be 950 kg/m³ and the liquid column above the diaphragm be 2.00 m. With the same g, the pressure is 18,632.635 Pa. If a calculation instead uses 1,000 kg/m³, it reports 1.90 m for that column: 0.10 m below the assumed actual height. This difference follows from the chosen density; it is not a measured sensor error or an estimate of a WESIVO model's performance.

Record where the density value comes from and the process conditions to which it applies. WIKA discusses density changes with temperature and composition. An adjustable density setting does not establish that an instrument measures density or compensates automatically when composition changes.

Keep height, offset and volume as separate configuration fields

Document the pressure reference and units, the adopted density and gravity basis, the diaphragm elevation, and the desired displayed datum. Specify where the offset is applied so it is not added twice. If the final quantity is volume, obtain a validated geometry or level-to-volume relationship; a level percentage alone does not establish a volume percentage for every tank shape. Test the calculation and receiver mapping against agreed reference values before interpreting deviations as a faulty probe.

What the WESIVO product information confirms

Published SL09A and SL09B entries identify submersible level-transmitter options. The SL09B entry includes adjustable density and range with LCD indication. Confirm the selected output, range basis, pressure reference, density-setting procedure, cable arrangement and media compatibility for the complete ordered version. This article does not assign density sensing, automatic composition compensation or tank-volume linearisation to either model. Use the linked application note to prepare the RFQ and handover record.

使用公式前先明确适用条件

本文讨论静止、密度已知且均匀的液体,容器敞口或有效通气,表压参考与液面处的大气压力一致。WIKA 的技术说明将静压与液柱高度及密度关联。加压容器、随高度变化的密度分布或不同压力参考,需要另行评审计算方法,不能将任意压力读数直接代入简化公式。

换算时统一单位

使用 h = p / (ρ × g)。其中 h 是感压膜片上方的液柱高度,单位 m;p 是表压,单位 Pa;ρ 是质量密度,单位 kg/m³;g 是重力加速度,单位 m/s²。先换算压力:1 kPa = 1,000 Pa,1 bar = 100,000 Pa。计算结果是长度,不是体积。若压力使用米水柱标注,也应核对该单位采用的密度与重力约定,不能将其直接理解为所有液体的实际高度。

算例一:液柱高度与水箱基准

以下均为假设算例,不是 WESIVO 产品量程、精度承诺或安装建议。设 ρ = 1,000 kg/m³,g = 9.80665 m/s²。当 p = 11,767.98 Pa 时,h = 11,767.98 / (1,000 × 9.80665) = 1.20 m,表示膜片上方的液柱高度。

定义 z 为膜片相对所选箱底基准的高度。若 z = 0.30 m,且膜片浸没,则液面相对该基准的高度为 H = z + h = 1.50 m。应在图纸上明确正负号约定。膜片高于箱底时,液面降到膜片以下,就不再具备相同的浸没液柱测量条件;添加偏置不能补出该区域的测量覆盖。

算例二:密度设置不符会改变结果

另设一组独立假设:实际均匀密度为 950 kg/m³,膜片上方液柱高度为 2.00 m,采用同一 g,则压力为 18,632.635 Pa。若计算时误用 1,000 kg/m³,得到的液柱高度是 1.90 m,比假设实际高度低 0.10 m。该差异来自密度取值,不是实测传感器误差,也不是对 WESIVO 某型号性能的估计。

记录密度值来源及其适用工况。WIKA 讨论了温度和介质组成变化对密度的影响。具有密度设置功能,不代表仪表能测量密度,也不代表介质组成变化时会自动补偿。

分开保存高度、偏置与体积配置

记录压力参考及单位、采用的密度与重力依据、膜片安装高度和要求显示的液位基准。明确偏置在哪个环节实施,避免重复相加。若最终需要体积,应取得经验证的几何数据或液位—体积关系;液位百分比并不适用于所有箱型的体积百分比。先用约定参考值核对计算和接收端映射,再判断偏差是否来自探头。

WESIVO 已发布信息确认了什么

SL09A、SL09B 页面列出了投入式液位变送器选项;SL09B 页面列有 LCD 显示、密度和量程可调。针对完整订购版本,仍应确认输出、量程依据、压力参考、密度设置方法、电缆结构及介质兼容性。本文不为任一型号添加密度测量、组成变化自动补偿或水箱容积线性化功能。可结合关联应用说明准备询价和交接记录。

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